diff --git a/HISTORY.rst b/HISTORY.rst
index 18188bc82..229d42ff0 100644
--- a/HISTORY.rst
+++ b/HISTORY.rst
@@ -7,6 +7,11 @@ Release History
 API Changes (Backward-Compatible)
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+- Added new ``UnknownFrameReceived`` event that fires when unknown extension
+  frames have been received. This only fires when using hyperframe 5.0 or
+  later: earlier versions of hyperframe cause us to silently ignore extension
+  frames.
+
 Bugfixes
 ~~~~~~~~
 
diff --git a/docs/source/api.rst b/docs/source/api.rst
index 56ca1213a..46e8a0faa 100644
--- a/docs/source/api.rst
+++ b/docs/source/api.rst
@@ -77,6 +77,9 @@ Events
 .. autoclass:: h2.events.AlternativeServiceAvailable
    :members:
 
+.. autoclass:: h2.events.UnknownFrameReceived
+   :members:
+
 
 Exceptions
 ----------
diff --git a/h2/connection.py b/h2/connection.py
index 5f9ccf84e..6a0d65ca4 100644
--- a/h2/connection.py
+++ b/h2/connection.py
@@ -23,13 +23,12 @@
 from .events import (
     WindowUpdated, RemoteSettingsChanged, PingAcknowledged,
     SettingsAcknowledged, ConnectionTerminated, PriorityUpdated,
-    AlternativeServiceAvailable,
+    AlternativeServiceAvailable, UnknownFrameReceived
 )
 from .exceptions import (
     ProtocolError, NoSuchStreamError, FlowControlError, FrameTooLargeError,
     TooManyStreamsError, StreamClosedError, StreamIDTooLowError,
-    NoAvailableStreamIDError, UnsupportedFrameError, RFC1122Error,
-    DenialOfServiceError
+    NoAvailableStreamIDError, RFC1122Error, DenialOfServiceError
 )
 from .frame_buffer import FrameBuffer
 from .settings import Settings, SettingCodes
@@ -46,6 +45,15 @@ class OversizedHeaderListError(Exception):
         pass
 
 
+try:
+    from hyperframe.frame import ExtensionFrame
+except ImportError:  # Platform-specific: Hyperframe < 5.0.0
+    # If the frame doesn't exist, that's just fine: we'll define it ourselves
+    # and the method will just never be called.
+    class ExtensionFrame(object):
+        pass
+
+
 class ConnectionState(Enum):
     IDLE = 0
     CLIENT_OPEN = 1
@@ -404,6 +412,7 @@ def __init__(self, client_side=True, header_encoding='utf-8', config=None):
             GoAwayFrame: self._receive_goaway_frame,
             ContinuationFrame: self._receive_naked_continuation,
             AltSvcFrame: self._receive_alt_svc_frame,
+            ExtensionFrame: self._receive_unknown_frame
         }
 
     def _prepare_for_sending(self, frames):
@@ -1575,10 +1584,6 @@ def _receive_frame(self, frame):
                 # Closed implicitly, also a connection error, but of type
                 # PROTOCOL_ERROR.
                 raise
-        except KeyError as e:  # pragma: no cover
-            # We don't have a function for handling this frame. Let's call this
-            # a PROTOCOL_ERROR and exit.
-            raise UnsupportedFrameError("Unexpected frame: %s" % frame)
         else:
             self._prepare_for_sending(frames)
 
@@ -1922,6 +1927,23 @@ def _receive_alt_svc_frame(self, frame):
 
         return frames, events
 
+    def _receive_unknown_frame(self, frame):
+        """
+        We have received a frame that we do not understand. This is almost
+        certainly an extension frame, though it's impossible to be entirely
+        sure.
+
+        RFC 7540 § 5.5 says that we MUST ignore unknown frame types: so we
+        do. We do notify the user that we received one, however.
+        """
+        # All we do here is log.
+        self.config.logger.debug(
+            "Received unknown extension frame (ID %d)", frame.stream_id
+        )
+        event = UnknownFrameReceived()
+        event.frame = frame
+        return [], [event]
+
     def _local_settings_acked(self):
         """
         Handle the local settings being ACKed, update internal state.
diff --git a/h2/events.py b/h2/events.py
index 55f202183..ff3ec3df3 100644
--- a/h2/events.py
+++ b/h2/events.py
@@ -574,6 +574,28 @@ def __repr__(self):
         )
 
 
+class UnknownFrameReceived(Event):
+    """
+    The UnknownFrameReceived event is fired when the remote peer sends a frame
+    that hyper-h2 does not understand. This occurs primarily when the remote
+    peer is employing HTTP/2 extensions that hyper-h2 doesn't know anything
+    about.
+
+    RFC 7540 requires that HTTP/2 implementations ignore these frames. hyper-h2
+    does so. However, this event is fired to allow implementations to perform
+    special processing on those frames if needed (e.g. if the implementation
+    is capable of handling the frame itself).
+
+    .. versionadded:: 2.7.0
+    """
+    def __init__(self):
+        #: The hyperframe Frame object that encapsulates the received frame.
+        self.frame = None
+
+    def __repr__(self):
+        return "<UnknownFrameReceived>"
+
+
 def _bytes_representation(data):
     """
     Converts a bytestring into something that is safe to print on all Python
diff --git a/h2/frame_buffer.py b/h2/frame_buffer.py
index cfa319860..bc1f7ca4e 100644
--- a/h2/frame_buffer.py
+++ b/h2/frame_buffer.py
@@ -65,11 +65,13 @@ def _parse_frame_header(self, data):
         """
         try:
             frame, length = Frame.parse_frame_header(data[:9])
-        except UnknownFrameError as e:
+        except UnknownFrameError as e:  # Platform-specific: Hyperframe < 5.0
             # Here we do something a bit odd. We want to consume the frame data
             # as consistently as possible, but we also don't ever want to yield
             # None. Instead, we make sure that, if there is no frame, we
             # recurse into ourselves.
+            # This can only happen now on older versions of hyperframe.
+            # TODO: Remove in 3.0
             length = e.length
             frame = None
         except ValueError as e:
diff --git a/setup.py b/setup.py
index eeda7d9f5..2ab40c699 100644
--- a/setup.py
+++ b/setup.py
@@ -62,7 +62,7 @@
         'Programming Language :: Python :: Implementation :: PyPy',
     ],
     install_requires=[
-        'hyperframe>=3.1, <5, !=4.0.0',
+        'hyperframe>=3.1, <6, !=4.0.0',
         'hpack>=2.2, <3',
     ],
     extras_require={
diff --git a/test/test_basic_logic.py b/test/test_basic_logic.py
index e9aee2669..ac34f760b 100644
--- a/test/test_basic_logic.py
+++ b/test/test_basic_logic.py
@@ -1574,8 +1574,10 @@ def test_unknown_frames_are_ignored(self, frame_factory, frame_id):
         f.type = frame_id
 
         events = c.receive_data(f.serialize())
-        assert not events
         assert not c.data_to_send()
+        assert len(events) == 1
+        assert isinstance(events[0], h2.events.UnknownFrameReceived)
+        assert isinstance(events[0].frame, hyperframe.frame.ExtensionFrame)
 
     def test_can_send_goaway_repeatedly(self, frame_factory):
         """
diff --git a/test/test_events.py b/test/test_events.py
index a4cbf809d..a40744908 100644
--- a/test/test_events.py
+++ b/test/test_events.py
@@ -323,6 +323,13 @@ def test_alternativeserviceavailable_repr(self):
             'field_value:h2=":8000"; ma=60>'
         )
 
+    def test_unknownframereceived_repr(self):
+        """
+        UnknownFrameReceived has a useful debug representation.
+        """
+        e = h2.events.UnknownFrameReceived()
+        assert repr(e) == '<UnknownFrameReceived>'
+
 
 def all_events():
     """