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Chrome developer tools now have the ability to list WebSocket frames and also inspect the data if the frames are not binary.
Process:
If your WebSocket connection uses binary frames then you will probably still want to use Wireshark to debug the connection. Wireshark 1.8.0 added dissector and filtering support for WebSockets. An alternative may be found in this other answer.
Chrome developer tools allows to see handshake request which stays pending during the opened connection, but you can't see traffic as far as I know. However you can sniff it for example.