diff --git a/lib/core/package.json b/lib/core/package.json
index 09254232d84e..37083420dadb 100644
--- a/lib/core/package.json
+++ b/lib/core/package.json
@@ -32,7 +32,9 @@
   "dependencies": {
     "@babel/plugin-proposal-class-properties": "^7.8.3",
     "@babel/plugin-proposal-export-default-from": "^7.8.3",
+    "@babel/plugin-proposal-nullish-coalescing-operator": "^7.10.1",
     "@babel/plugin-proposal-object-rest-spread": "^7.9.6",
+    "@babel/plugin-proposal-optional-chaining": "^7.10.1",
     "@babel/plugin-proposal-private-methods": "^7.8.3",
     "@babel/plugin-syntax-dynamic-import": "^7.8.3",
     "@babel/plugin-transform-arrow-functions": "^7.8.3",
diff --git a/lib/core/src/server/common/babel.js b/lib/core/src/server/common/babel.js
index 84202a283272..18a0afed1728 100644
--- a/lib/core/src/server/common/babel.js
+++ b/lib/core/src/server/common/babel.js
@@ -16,6 +16,14 @@ export const plugins = [
   require.resolve('@babel/plugin-transform-spread'),
   require.resolve('@babel/plugin-transform-for-of'),
   require.resolve('babel-plugin-macros'),
+  /*
+   * Optional chaining and nullish coalescing are supported in
+   * @babel/preset-env, but not yet supported in Webpack due to support
+   * missing from acorn. These can be removed once Webpack has support.
+   * See https://github.com/facebook/create-react-app/issues/8445#issuecomment-588512250
+   */
+  require.resolve('@babel/plugin-proposal-optional-chaining'),
+  require.resolve('@babel/plugin-proposal-nullish-coalescing-operator'),
 ];
 
 export const presets = [
diff --git a/yarn.lock b/yarn.lock
index dd8a457f1108..0ced7d48b282 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -727,6 +727,11 @@
   resolved "https://registry.yarnpkg.com/@babel/helper-plugin-utils/-/helper-plugin-utils-7.8.3.tgz#9ea293be19babc0f52ff8ca88b34c3611b208670"
   integrity sha512-j+fq49Xds2smCUNYmEHF9kGNkhbet6yVIBp4e6oeQpH1RUs/Ir06xUKzDjDkGcaaokPiTNs2JBWHjaE4csUkZQ==
 
+"@babel/helper-plugin-utils@^7.10.1":
+  version "7.10.1"
+  resolved "https://registry.yarnpkg.com/@babel/helper-plugin-utils/-/helper-plugin-utils-7.10.1.tgz#ec5a5cf0eec925b66c60580328b122c01230a127"
+  integrity sha512-fvoGeXt0bJc7VMWZGCAEBEMo/HAjW2mP8apF5eXK0wSqwLAVHAISCWRoLMBMUs2kqeaG77jltVqu4Hn8Egl3nA==
+
 "@babel/helper-regex@^7.8.3":
   version "7.8.3"
   resolved "https://registry.yarnpkg.com/@babel/helper-regex/-/helper-regex-7.8.3.tgz#139772607d51b93f23effe72105b319d2a4c6965"
@@ -908,6 +913,14 @@
     "@babel/helper-plugin-utils" "^7.8.3"
     "@babel/plugin-syntax-nullish-coalescing-operator" "^7.8.0"
 
+"@babel/plugin-proposal-nullish-coalescing-operator@^7.10.1":
+  version "7.10.1"
+  resolved "https://registry.yarnpkg.com/@babel/plugin-proposal-nullish-coalescing-operator/-/plugin-proposal-nullish-coalescing-operator-7.10.1.tgz#02dca21673842ff2fe763ac253777f235e9bbf78"
+  integrity sha512-56cI/uHYgL2C8HVuHOuvVowihhX0sxb3nnfVRzUeVHTWmRHTZrKuAh/OBIMggGU/S1g/1D2CRCXqP+3u7vX7iA==
+  dependencies:
+    "@babel/helper-plugin-utils" "^7.10.1"
+    "@babel/plugin-syntax-nullish-coalescing-operator" "^7.8.0"
+
 "@babel/plugin-proposal-numeric-separator@7.8.3", "@babel/plugin-proposal-numeric-separator@^7.8.3":
   version "7.8.3"
   resolved "https://registry.yarnpkg.com/@babel/plugin-proposal-numeric-separator/-/plugin-proposal-numeric-separator-7.8.3.tgz#5d6769409699ec9b3b68684cd8116cedff93bad8"
@@ -941,6 +954,14 @@
     "@babel/helper-plugin-utils" "^7.8.3"
     "@babel/plugin-syntax-optional-chaining" "^7.8.0"
 
+"@babel/plugin-proposal-optional-chaining@^7.10.1":
+  version "7.10.1"
+  resolved "https://registry.yarnpkg.com/@babel/plugin-proposal-optional-chaining/-/plugin-proposal-optional-chaining-7.10.1.tgz#15f5d6d22708629451a91be28f8facc55b0e818c"
+  integrity sha512-dqQj475q8+/avvok72CF3AOSV/SGEcH29zT5hhohqqvvZ2+boQoOr7iGldBG5YXTO2qgCgc2B3WvVLUdbeMlGA==
+  dependencies:
+    "@babel/helper-plugin-utils" "^7.10.1"
+    "@babel/plugin-syntax-optional-chaining" "^7.8.0"
+
 "@babel/plugin-proposal-private-methods@^7.3.3", "@babel/plugin-proposal-private-methods@^7.8.3":
   version "7.8.3"
   resolved "https://registry.yarnpkg.com/@babel/plugin-proposal-private-methods/-/plugin-proposal-private-methods-7.8.3.tgz#01248c6c8dc292116b3b4ebd746150f4f0728bab"