diff --git a/internal/protocol/protocol.go b/internal/protocol/protocol.go
index c18a2b65c..6e59afcb4 100644
--- a/internal/protocol/protocol.go
+++ b/internal/protocol/protocol.go
@@ -64,6 +64,10 @@ const MinStatelessResetSize = 1 /* first byte */ + 22 /* random bytes */ + 16 /*
 // MinConnectionIDLenInitial is the minimum length of the destination connection ID on an Initial packet.
 const MinConnectionIDLenInitial = 8
 
+// MaxStreamCount is the maximum stream count value that can be sent in MAX_STREAMS frames
+// and as the stream count in the transport parameters
+const MaxStreamCount = 1 << 60
+
 // DefaultAckDelayExponent is the default ack delay exponent
 const DefaultAckDelayExponent = 3
 
diff --git a/streams_map.go b/streams_map.go
index b71953756..b47596de6 100644
--- a/streams_map.go
+++ b/streams_map.go
@@ -8,6 +8,7 @@ import (
 	"github.com/lucas-clemente/quic-go/internal/flowcontrol"
 	"github.com/lucas-clemente/quic-go/internal/handshake"
 	"github.com/lucas-clemente/quic-go/internal/protocol"
+	"github.com/lucas-clemente/quic-go/internal/qerr"
 	"github.com/lucas-clemente/quic-go/internal/wire"
 )
 
@@ -159,6 +160,9 @@ func (m *streamsMap) GetOrOpenSendStream(id protocol.StreamID) (sendStreamI, err
 }
 
 func (m *streamsMap) HandleMaxStreamsFrame(f *wire.MaxStreamsFrame) error {
+	if f.MaxStreams > protocol.MaxStreamCount {
+		return qerr.StreamLimitError
+	}
 	id := protocol.MaxStreamID(f.Type, f.MaxStreams, m.perspective)
 	switch id.Type() {
 	case protocol.StreamTypeUni:
diff --git a/streams_map_test.go b/streams_map_test.go
index 15df4c269..19f16b7bb 100644
--- a/streams_map_test.go
+++ b/streams_map_test.go
@@ -356,6 +356,13 @@ var _ = Describe("Streams Map", func() {
 					_, err = m.OpenUniStream()
 					expectTooManyStreamsError(err)
 				})
+
+				It("rejects MAX_STREAMS frames with too large values", func() {
+					Expect(m.HandleMaxStreamsFrame(&wire.MaxStreamsFrame{
+						Type:       protocol.StreamTypeBidi,
+						MaxStreams: protocol.MaxStreamCount + 1,
+					})).To(MatchError(qerr.StreamLimitError))
+				})
 			})
 
 			Context("sending MAX_STREAMS frames", func() {