Almost exactly one year ago Blizzard revealed that it was working on a voice chat system for its Battle.net client that would enable players to talk to one another while grinding their favorite Blizzard game—or, I suppose, just hanging out in Battle.net, as one sometimes does. Testing began earlier this year, and today the studio announced that the feature, now called Blizzard Voice in accordance with the recent "no more Battle.net" edict, is available to everyone.
Blizzard Voice doesn't allow for wide-open chat, as the system is limited to friends, and friends of friends. That may cut down on grief from trolls, but it also rather severely limits its functionality in pick-up games. It runs in the background, so you chat while you play, but it does not currently interact with Overwatch voice channels. There's some speculation in various Reddit threads (like this one, for instance) that full in-game chat functionality will be added at some point in the future, but for now you're probably going to want to hang on to your favorite stand-alone voice app.
To try Blizzard Voice for yourself, update your Battle.net client, open your friends list, select "Create a Channel," and then invite all your pals. Alternatively, for a spot of one-on-one conversation, you can simply right-click a name in your list and select "Start a Voice Chat."