diff --git a/synapse/app/_base.py b/synapse/app/_base.py
index d4c6c4c8e2..08199a5e8d 100644
--- a/synapse/app/_base.py
+++ b/synapse/app/_base.py
@@ -22,13 +22,14 @@ import traceback
 import psutil
 from daemonize import Daemonize
 
-from twisted.internet import error, reactor
+from twisted.internet import defer, error, reactor
 from twisted.protocols.tls import TLSMemoryBIOFactory
 
 import synapse
 from synapse.app import check_bind_error
 from synapse.crypto import context_factory
 from synapse.util import PreserveLoggingContext
+from synapse.util.async_helpers import Linearizer
 from synapse.util.rlimit import change_resource_limit
 from synapse.util.versionstring import get_version_string
 
@@ -99,6 +100,8 @@ def start_reactor(
         logger (logging.Logger): logger instance to pass to Daemonize
     """
 
+    install_dns_limiter(reactor)
+
     def run():
         # make sure that we run the reactor with the sentinel log context,
         # otherwise other PreserveLoggingContext instances will get confused
@@ -312,3 +315,81 @@ def setup_sentry(hs):
         name = hs.config.worker_name if hs.config.worker_name else "master"
         scope.set_tag("worker_app", app)
         scope.set_tag("worker_name", name)
+
+
+def install_dns_limiter(reactor, max_dns_requests_in_flight=100):
+    """Replaces the resolver with one that limits the number of in flight DNS
+    requests.
+
+    This is to workaround https://twistedmatrix.com/trac/ticket/9620, where we
+    can run out of file descriptors and infinite loop if we attempt to do too
+    many DNS queries at once
+    """
+    new_resolver = _LimitedHostnameResolver(
+        reactor.nameResolver, max_dns_requests_in_flight,
+    )
+
+    reactor.installNameResolver(new_resolver)
+
+
+class _LimitedHostnameResolver(object):
+    """Wraps a IHostnameResolver, limiting the number of in-flight DNS lookups.
+    """
+
+    def __init__(self, resolver, max_dns_requests_in_flight):
+        self._resolver = resolver
+        self._limiter = Linearizer(
+            name="dns_client_limiter", max_count=max_dns_requests_in_flight,
+        )
+
+    def resolveHostName(self, resolutionReceiver, hostName, portNumber=0,
+                        addressTypes=None, transportSemantics='TCP'):
+        # Note this is happening deep within the reactor, so we don't need to
+        # worry about log contexts.
+
+        # We need this function to return `resolutionReceiver` so we do all the
+        # actual logic involving deferreds in a separate function.
+        self._resolve(
+            resolutionReceiver, hostName, portNumber,
+            addressTypes, transportSemantics,
+        )
+
+        return resolutionReceiver
+
+    @defer.inlineCallbacks
+    def _resolve(self, resolutionReceiver, hostName, portNumber=0,
+                 addressTypes=None, transportSemantics='TCP'):
+
+        with (yield self._limiter.queue(())):
+            # resolveHostName doesn't return a Deferred, so we need to hook into
+            # the receiver interface to get told when resolution has finished.
+
+            deferred = defer.Deferred()
+            receiver = _DeferredResolutionReceiver(resolutionReceiver, deferred)
+
+            self._resolver.resolveHostName(
+                receiver, hostName, portNumber,
+                addressTypes, transportSemantics,
+            )
+
+            yield deferred
+
+
+class _DeferredResolutionReceiver(object):
+    """Wraps a IResolutionReceiver and simply resolves the given deferred when
+    resolution is complete
+    """
+
+    def __init__(self, receiver, deferred):
+        self._receiver = receiver
+        self._deferred = deferred
+
+    def resolutionBegan(self, resolutionInProgress):
+        self._receiver.resolutionBegan(resolutionInProgress)
+
+    def addressResolved(self, address):
+        self._receiver.addressResolved(address)
+
+    def resolutionComplete(self):
+        self._deferred.callback(())
+        self._receiver.resolutionComplete()