diff --git a/pkg/sql/opt/memo/expr_format.go b/pkg/sql/opt/memo/expr_format.go
index 578df2821779..66b89e3e9665 100644
--- a/pkg/sql/opt/memo/expr_format.go
+++ b/pkg/sql/opt/memo/expr_format.go
@@ -1512,6 +1512,9 @@ func FormatPrivate(f *ExprFmtCtx, private interface{}, physProps *physical.Requi
 	case *FunctionPrivate:
 		fmt.Fprintf(f.Buffer, " %s", t.Name)
 
+	case *UserDefinedFunctionPrivate:
+		fmt.Fprintf(f.Buffer, " %s", t.Name)
+
 	case *WindowsItemPrivate:
 		fmt.Fprintf(f.Buffer, " frame=%q", &t.Frame)
 
diff --git a/pkg/sql/opt/norm/decorrelate_funcs.go b/pkg/sql/opt/norm/decorrelate_funcs.go
index 746aa48606c8..3701732275e4 100644
--- a/pkg/sql/opt/norm/decorrelate_funcs.go
+++ b/pkg/sql/opt/norm/decorrelate_funcs.go
@@ -62,6 +62,10 @@ func (c *CustomFuncs) deriveHasHoistableSubquery(scalar opt.ScalarExpr) bool {
 		// WHERE clause, it will be transformed to an Exists operator, so this case
 		// only occurs when the Any is nested, in a projection, etc.
 		return !t.Input.Relational().OuterCols.Empty()
+
+	case *memo.UserDefinedFunctionExpr:
+		// Do not attempt to hoist UDFs.
+		return false
 	}
 
 	// If HasHoistableSubquery is true for any child, then it's true for this
diff --git a/pkg/sql/opt/norm/testdata/rules/udf b/pkg/sql/opt/norm/testdata/rules/udf
new file mode 100644
index 000000000000..8548518c233b
--- /dev/null
+++ b/pkg/sql/opt/norm/testdata/rules/udf
@@ -0,0 +1,21 @@
+exec-ddl
+CREATE FUNCTION one() RETURNS INT LANGUAGE SQL AS 'SELECT 1';
+----
+
+# Do not attempt to hoist UDFs.
+norm
+SELECT one()
+----
+values
+ ├── columns: one:2
+ ├── cardinality: [1 - 1]
+ ├── key: ()
+ ├── fd: ()-->(2)
+ └── tuple
+      └── user-defined-function: one
+           └── values
+                ├── columns: "?column?":1!null
+                ├── cardinality: [1 - 1]
+                ├── key: ()
+                ├── fd: ()-->(1)
+                └── (1,)
diff --git a/pkg/sql/opt/ops/scalar.opt b/pkg/sql/opt/ops/scalar.opt
index dcf85083cc5e..7abbc35d6c81 100644
--- a/pkg/sql/opt/ops/scalar.opt
+++ b/pkg/sql/opt/ops/scalar.opt
@@ -1214,6 +1214,21 @@ define NthValue {
     Nth ScalarExpr
 }
 
+# UserDefinedFunction invokes a user-defined function. The
+# UserDefinedFunctionPrivate field contains the name of the function and a
+# pointer to its type.
+[Scalar]
+define UserDefinedFunction {
+    Body RelExpr
+    _ UserDefinedFunctionPrivate
+}
+
+[Private]
+define UserDefinedFunctionPrivate {
+    Name string
+    Typ Type
+}
+
 # KVOptions is a set of KVOptionItems that specify arbitrary keys and values
 # that are used as modifiers for various statements (see tree.KVOptions). The
 # key is a constant string but the value can be a scalar expression.
diff --git a/pkg/sql/opt/optbuilder/scalar.go b/pkg/sql/opt/optbuilder/scalar.go
index c6b50b81571f..41b8eb0bd115 100644
--- a/pkg/sql/opt/optbuilder/scalar.go
+++ b/pkg/sql/opt/optbuilder/scalar.go
@@ -21,6 +21,7 @@ import (
 	"github.com/cockroachdb/cockroach/pkg/sql/opt/cat"
 	"github.com/cockroachdb/cockroach/pkg/sql/opt/memo"
 	"github.com/cockroachdb/cockroach/pkg/sql/opt/norm"
+	"github.com/cockroachdb/cockroach/pkg/sql/parser"
 	"github.com/cockroachdb/cockroach/pkg/sql/pgwire/pgcode"
 	"github.com/cockroachdb/cockroach/pkg/sql/pgwire/pgerror"
 	"github.com/cockroachdb/cockroach/pkg/sql/privilege"
@@ -529,6 +530,10 @@ func (b *Builder) buildFunction(
 		panic(err)
 	}
 
+	if f.ResolvedOverload().Body != "" {
+		return b.buildUDF(f, def, inScope, outScope, outCol)
+	}
+
 	if isAggregate(def) {
 		panic(errors.AssertionFailedf("aggregate function should have been replaced"))
 	}
@@ -583,6 +588,35 @@ func (b *Builder) buildFunction(
 	return b.finishBuildScalar(f, out, inScope, outScope, outCol)
 }
 
+// buildUDF builds a set of memo groups that represents a user-defined function
+// invocation.
+// TODO(mgartner): Support multi-statement UDFs.
+// TODO(mgartner): Support UDFs with arguments.
+func (b *Builder) buildUDF(
+	f *tree.FuncExpr, def *tree.FunctionDefinition, inScope, outScope *scope, outCol *scopeColumn,
+) (out opt.ScalarExpr) {
+	stmt, err := parser.ParseOne(f.ResolvedOverload().Body)
+	if err != nil {
+		panic(err)
+	}
+
+	// A statement inside a UDF body cannot refer to anything from the outer
+	// expression calling the function, so we use an empty scope.
+	// TODO(mgartner): We may need to set bodyScope.atRoot=true to prevent CTEs
+	// that mutate and are not at the top-level.
+	bodyScope := b.allocScope()
+	bodyScope = b.buildStmt(stmt.AST, nil /* desiredTypes */, bodyScope)
+
+	out = b.factory.ConstructUserDefinedFunction(
+		bodyScope.expr,
+		&memo.UserDefinedFunctionPrivate{
+			Name: def.Name,
+			Typ:  f.ResolvedType(),
+		},
+	)
+	return b.finishBuildScalar(f, out, inScope, outScope, outCol)
+}
+
 // buildRangeCond builds a RANGE clause as a simpler expression. Examples:
 // x BETWEEN a AND b                ->  x >= a AND x <= b
 // x NOT BETWEEN a AND b            ->  NOT (x >= a AND x <= b)
diff --git a/pkg/sql/opt/optbuilder/testdata/udf b/pkg/sql/opt/optbuilder/testdata/udf
new file mode 100644
index 000000000000..a370e8ee357a
--- /dev/null
+++ b/pkg/sql/opt/optbuilder/testdata/udf
@@ -0,0 +1,68 @@
+exec-ddl
+CREATE TABLE abc (
+  a INT PRIMARY KEY,
+  b INT,
+  c INT
+)
+----
+
+build
+SELECT foo()
+----
+error (42883): unknown function: foo
+
+exec-ddl
+CREATE FUNCTION one() RETURNS INT LANGUAGE SQL AS 'SELECT 1';
+----
+
+build
+SELECT one()
+----
+project
+ ├── columns: one:2
+ ├── values
+ │    └── ()
+ └── projections
+      └── user-defined-function: one [as=one:2]
+           └── project
+                ├── columns: "?column?":1!null
+                ├── values
+                │    └── ()
+                └── projections
+                     └── 1 [as="?column?":1]
+
+build
+SELECT *, one() FROM abc
+----
+project
+ ├── columns: a:1!null b:2 c:3 one:7
+ ├── scan abc
+ │    └── columns: a:1!null b:2 c:3 crdb_internal_mvcc_timestamp:4 tableoid:5
+ └── projections
+      └── user-defined-function: one [as=one:7]
+           └── project
+                ├── columns: "?column?":6!null
+                ├── values
+                │    └── ()
+                └── projections
+                     └── 1 [as="?column?":6]
+
+build
+SELECT * FROM abc WHERE one() = c
+----
+project
+ ├── columns: a:1!null b:2 c:3
+ └── select
+      ├── columns: a:1!null b:2 c:3 crdb_internal_mvcc_timestamp:4 tableoid:5
+      ├── scan abc
+      │    └── columns: a:1!null b:2 c:3 crdb_internal_mvcc_timestamp:4 tableoid:5
+      └── filters
+           └── eq
+                ├── user-defined-function: one
+                │    └── project
+                │         ├── columns: "?column?":6!null
+                │         ├── values
+                │         │    └── ()
+                │         └── projections
+                │              └── 1 [as="?column?":6]
+                └── c:3
diff --git a/pkg/sql/opt/testutils/opttester/opt_tester.go b/pkg/sql/opt/testutils/opttester/opt_tester.go
index c9af74dd8d31..9fec4efa2ce4 100644
--- a/pkg/sql/opt/testutils/opttester/opt_tester.go
+++ b/pkg/sql/opt/testutils/opttester/opt_tester.go
@@ -274,6 +274,7 @@ func New(catalog cat.Catalog, sql string) *OptTester {
 		semaCtx: tree.MakeSemaContext(),
 		evalCtx: eval.MakeTestingEvalContext(cluster.MakeTestingClusterSettings()),
 	}
+	ot.semaCtx.SearchPath = tree.EmptySearchPath
 	ot.semaCtx.FunctionResolver = ot.catalog
 	// To allow opttester tests to use now(), we hardcode a preset transaction
 	// time. May 10, 2017 is a historic day: the release date of CockroachDB 1.0.