diff --git a/src/OpenSSL/SSL.py b/src/OpenSSL/SSL.py
index d4158d4..8bbde5b 100644
--- a/src/OpenSSL/SSL.py
+++ b/src/OpenSSL/SSL.py
@@ -1455,6 +1455,8 @@
             buf = str(buf)
         if not isinstance(buf, bytes):
             raise TypeError("data must be a memoryview, buffer or byte string")
+        if len(buf) > 2147483647:
+            raise ValueError("Cannot send more than 2**31-1 bytes at once.")
 
         result = _lib.SSL_write(self._ssl, buf, len(buf))
         self._raise_ssl_error(self._ssl, result)
@@ -1486,7 +1488,13 @@
         data = _ffi.new("char[]", buf)
 
         while left_to_send:
-            result = _lib.SSL_write(self._ssl, data + total_sent, left_to_send)
+            # SSL_write's num arg is an int,
+            # so we cannot send more than 2**31-1 bytes at once.
+            result = _lib.SSL_write(
+                self._ssl,
+                data + total_sent,
+                min(left_to_send, 2147483647)
+            )
             self._raise_ssl_error(self._ssl, result)
             total_sent += result
             left_to_send -= result
diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index d2a56b7..44a042b 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -6,6 +6,7 @@
 """
 
 import datetime
+import sys
 import uuid
 
 from gc import collect, get_referrers
@@ -2662,6 +2663,14 @@
             assert isinstance(cipher, str)
 
 
+class VeryLarge(bytes):
+    """
+    Mock object so that we don't have to allocate 2**31 bytes
+    """
+    def __len__(self):
+        return 2**31
+
+
 class TestConnectionSend(object):
     """
     Tests for `Connection.send`.
@@ -2725,6 +2734,21 @@
         assert count == 2
         assert client.recv(2) == b'xy'
 
+    @pytest.mark.skipif(
+        sys.maxsize < 2**31,
+        reason="sys.maxsize < 2**31 - test requires 64 bit"
+    )
+    def test_buf_too_large(self):
+        """
+        When passed a buffer containing >= 2**31 bytes,
+        `Connection.send` bails out as SSL_write only
+        accepts an int for the buffer length.
+        """
+        connection = Connection(Context(TLSv1_METHOD), None)
+        with pytest.raises(ValueError) as exc_info:
+            connection.send(VeryLarge())
+        exc_info.match(r"Cannot send more than .+ bytes at once")
+
 
 def _make_memoryview(size):
     """