diff --git a/h11/_connection.py b/h11/_connection.py
index e37d82a..d8ede96 100644
--- a/h11/_connection.py
+++ b/h11/_connection.py
@@ -478,6 +478,7 @@ def next_event(self) -> Union[Event, Type[NEED_DATA], Type[PAUSED]]:
         if self.their_state is ERROR:
             raise RemoteProtocolError("Can't receive data when peer state is ERROR")
         try:
+            receive_buffer_len_before = len(self._receive_buffer)
             event = self._extract_next_receive_event()
             if event not in [NEED_DATA, PAUSED]:
                 self._process_event(self.their_role, cast(Event, event))
@@ -492,6 +493,15 @@ def next_event(self) -> Union[Event, Type[NEED_DATA], Type[PAUSED]]:
                     # We're still trying to complete some event, but that's
                     # never going to happen because no more data is coming
                     raise RemoteProtocolError("peer unexpectedly closed connection")
+
+            if isinstance(event, (Request, InformationalResponse, Response)):
+                read_from_buffer = receive_buffer_len_before - len(self._receive_buffer)
+                if read_from_buffer > self._max_incomplete_event_size + 1:
+                    # 431 is "Request header fields too large" which is pretty
+                    # much the only situation where we can get here
+                    raise RemoteProtocolError(
+                        "Receive buffer too long", error_status_hint=431
+                    )
             return event
         except BaseException as exc:
             self._process_error(self.their_role)
diff --git a/h11/tests/test_connection.py b/h11/tests/test_connection.py
index 01260dc..b7923c3 100644
--- a/h11/tests/test_connection.py
+++ b/h11/tests/test_connection.py
@@ -486,6 +486,22 @@ def test_max_incomplete_event_size_countermeasure() -> None:
         c.next_event()
 
 
+@pytest.mark.parametrize("chunking", [False, True])
+def test_max_incomplete_event_size_enforced_regardless_of_chunking(chunking) -> None:
+    buffer = b"GET / HTTP/1.0\r\nBig: " + b"a" * 4000 + b"\r\n\r\n"
+    c = Connection(SERVER, max_incomplete_event_size=(len(buffer) - 2))
+
+    if chunking:
+        chunks = [buffer[:-1], buffer[-1:]]
+    else:
+        chunks = [buffer]
+
+    with pytest.raises(RemoteProtocolError):
+        for chunk in chunks:
+            c.receive_data(chunk)
+            get_all_events(c)
+
+
 def test_reuse_simple() -> None:
     p = ConnectionPair()
     p.send(