diff --git a/distributed/comm/tcp.py b/distributed/comm/tcp.py
index de6cee016d8..1b8c063f58f 100644
--- a/distributed/comm/tcp.py
+++ b/distributed/comm/tcp.py
@@ -1,3 +1,4 @@
+import ctypes
 import errno
 import functools
 import logging
@@ -14,6 +15,7 @@
 except ImportError:
     ssl = None
 
+from tlz import sliding_window
 from tornado import netutil
 from tornado.iostream import StreamClosedError
 from tornado.tcpclient import TCPClient
@@ -35,6 +37,7 @@
 
 
 MAX_BUFFER_SIZE = MEMORY_LIMIT / 2
+C_MAX_INT = 256 ** ctypes.sizeof(ctypes.c_int) // 2 - 1
 
 
 def set_tcp_timeout(comm):
@@ -193,9 +196,15 @@ async def read(self, deserializers=None):
             frames_nbytes = await stream.read_bytes(fmt_size)
             (frames_nbytes,) = struct.unpack(fmt, frames_nbytes)
 
-            frames = bytearray(frames_nbytes)
-            n = await stream.read_into(frames)
-            assert n == frames_nbytes, (n, frames_nbytes)
+            frames = memoryview(bytearray(frames_nbytes))
+            # Workaround for OpenSSL 1.0.2 (can drop with OpenSSL 1.1.1)
+            for i, j in sliding_window(
+                2, range(0, frames_nbytes + C_MAX_INT, C_MAX_INT)
+            ):
+                chunk = frames[i:j]
+                chunk_nbytes = len(chunk)
+                n = await stream.read_into(chunk)
+                assert n == chunk_nbytes, (n, chunk_nbytes)
         except StreamClosedError as e:
             self.stream = None
             self._closed = True