Comment by vladimirralev

TURN/ICE is supposed to work just fine on symmetric NATs. Chrome even supports single-socket TCP relays, which can't be broken easily by any sane firewall. I personally have a few boxes testing it with only TCP 80 port allowed and it still finds a way to connect. A few tricks on the TURN side have to be employed but it's pretty robust. Whatever issue the OP has to be a bug or configuration issue. There are known problems and I still see a lot of freezes, protocol or hardware compatibility issues, CPU overload and so on, but straight Chrome to Chrome connections seem robust.