diff --git a/ssl/s3_clnt.c b/ssl/s3_clnt.c
index b474352..eb96780 100644
--- a/ssl/s3_clnt.c
+++ b/ssl/s3_clnt.c
@@ -1168,6 +1168,13 @@
       OPENSSL_PUT_ERROR(SSL, SSL_R_BAD_DH_P_LENGTH);
       goto err;
     }
+    if (s->session->key_exchange_info > 4096) {
+      /* Overly large DHE groups are prohibitively expensive, so enforce a limit
+       * to prevent a server from causing us to perform too expensive of a
+       * computation. */
+      OPENSSL_PUT_ERROR(SSL, SSL_R_DH_P_TOO_LONG);
+      goto err;
+    }
     DH_free(s->s3->tmp.peer_dh_tmp);
     s->s3->tmp.peer_dh_tmp = dh;
     dh = NULL;
diff --git a/ssl/test/runner/runner.go b/ssl/test/runner/runner.go
index 6573871..a1801c8 100644
--- a/ssl/test/runner/runner.go
+++ b/ssl/test/runner/runner.go
@@ -2167,9 +2167,25 @@
 			},
 		},
 		shouldFail:    true,
-		expectedError: "BAD_DH_P_LENGTH",
+		expectedError: ":BAD_DH_P_LENGTH:",
 	})
 
+	testCases = append(testCases, testCase{
+		name: "SillyDH",
+		config: Config{
+			CipherSuites: []uint16{TLS_DHE_RSA_WITH_AES_128_GCM_SHA256},
+			Bugs: ProtocolBugs{
+				// This is a 4097-bit prime number, generated
+				// with:
+				// openssl gendh 4097 | openssl asn1parse -i
+				DHGroupPrime: bigFromHex("01D366FA64A47419B0CD4A45918E8D8C8430F674621956A9F52B0CA592BC104C6E38D60C58F2CA66792A2B7EBDC6F8FFE75AB7D6862C261F34E96A2AEEF53AB7C21365C2E8FB0582F71EB57B1C227C0E55AE859E9904A25EFECD7B435C4D4357BD840B03649D4A1F8037D89EA4E1967DBEEF1CC17A6111C48F12E9615FFF336D3F07064CB17C0B765A012C850B9E3AA7A6984B96D8C867DDC6D0F4AB52042572244796B7ECFF681CD3B3E2E29AAECA391A775BEE94E502FB15881B0F4AC60314EA947C0C82541C3D16FD8C0E09BB7F8F786582032859D9C13187CE6C0CB6F2D3EE6C3C9727C15F14B21D3CD2E02BDB9D119959B0E03DC9E5A91E2578762300B1517D2352FC1D0BB934A4C3E1B20CE9327DB102E89A6C64A8C3148EDFC5A94913933853442FA84451B31FD21E492F92DD5488E0D871AEBFE335A4B92431DEC69591548010E76A5B365D346786E9A2D3E589867D796AA5E25211201D757560D318A87DFB27F3E625BC373DB48BF94A63161C674C3D4265CB737418441B7650EABC209CF675A439BEB3E9D1AA1B79F67198A40CEFD1C89144F7D8BAF61D6AD36F466DA546B4174A0E0CAF5BD788C8243C7C2DDDCC3DB6FC89F12F17D19FBD9B0BC76FE92891CD6BA07BEA3B66EF12D0D85E788FD58675C1B0FBD16029DCC4D34E7A1A41471BDEDF78BF591A8B4E96D88BEC8EDC093E616292BFC096E69A916E8D624B"),
+			},
+		},
+		shouldFail:    true,
+		expectedError: ":DH_P_TOO_LONG:",
+	})
+
+
 	// versionSpecificCiphersTest specifies a test for the TLS 1.0 and TLS
 	// 1.1 specific cipher suite settings. A server is setup with the given
 	// cipher lists and then a connection is made for each member of