My group has been running together through normal then through NM. About half way through act one we started receiving Error 3006 when trying to type in party chat. DC'd one player and just shows a time out error for me.
I figured out a solution to this error while I was logging into Diablo 3. I got onto World of Warcraft and logged in 1 of my toons on there. Then, I exited and retried Diablo 3... and BAM it works! I imagine logging into a trial version of WoW for those who don't have it under your Battlenet account, or even logging into Starcraft 2.