diff --git a/docs/source/reference-io.rst b/docs/source/reference-io.rst
index d6e5ff7b7d..723ecd78e9 100644
--- a/docs/source/reference-io.rst
+++ b/docs/source/reference-io.rst
@@ -403,6 +403,10 @@ Socket objects
          left in an unknown state – possibly open, and possibly
          closed. The only reasonable thing to do is to close it.
 
+   .. method:: is_readable
+
+      Check whether the socket is readable or not.
+
    .. method:: sendfile
 
       `Not implemented yet! <https://github.com/python-trio/trio/issues/45>`__
diff --git a/newsfragments/760.feature.rst b/newsfragments/760.feature.rst
new file mode 100644
index 0000000000..dd7ab9d34b
--- /dev/null
+++ b/newsfragments/760.feature.rst
@@ -0,0 +1,2 @@
+Trio sockets have a new method `~trio.socket.SocketType.is_readable` that allows
+you to check whether a socket is readable. This is useful for HTTP/1.1 clients.
diff --git a/trio/_socket.py b/trio/_socket.py
index e866213ffa..0e257849b0 100644
--- a/trio/_socket.py
+++ b/trio/_socket.py
@@ -1,5 +1,6 @@
 import os as _os
 import sys as _sys
+import select
 import socket as _stdlib_socket
 from functools import wraps as _wraps
 
@@ -289,7 +290,7 @@ def socket(
 
 def _sniff_sockopts_for_fileno(family, type, proto, fileno):
     """Correct SOCKOPTS for given fileno, falling back to provided values.
-    
+
     """
     # Wrap the raw fileno into a Python socket object
     # This object might have the wrong metadata, but it lets us easily call getsockopt
@@ -478,6 +479,15 @@ def shutdown(self, flag):
         if flag in [_stdlib_socket.SHUT_WR, _stdlib_socket.SHUT_RDWR]:
             self._did_shutdown_SHUT_WR = True
 
+    def is_readable(self):
+        # use select.select on Windows, and select.poll everywhere else
+        if _sys.platform == "win32":
+            rready, _, _ = select.select([self._sock], [], [], 0)
+            return bool(rready)
+        p = select.poll()
+        p.register(self._sock, select.POLLIN)
+        return bool(p.poll(0))
+
     async def wait_writable(self):
         await _core.wait_writable(self._sock)
 
diff --git a/trio/tests/test_socket.py b/trio/tests/test_socket.py
index beab12a999..c03c8bb8ff 100644
--- a/trio/tests/test_socket.py
+++ b/trio/tests/test_socket.py
@@ -404,6 +404,17 @@ async def test_SocketType_simple_server(address, socket_type):
             assert await client.recv(1) == b"x"
 
 
+async def test_SocketType_is_readable():
+    a, b = tsocket.socketpair()
+    with a, b:
+        assert not a.is_readable()
+        await b.send(b"x")
+        await _core.wait_readable(a)
+        assert a.is_readable()
+        assert await a.recv(1) == b"x"
+        assert not a.is_readable()
+
+
 # On some macOS systems, getaddrinfo likes to return V4-mapped addresses even
 # when we *don't* pass AI_V4MAPPED.
 # https://github.com/python-trio/trio/issues/580