Go into your setting in game. Find something that says automatic chat or fireteam chat. It should be on of the left options in the settings menu. If this doesn't work, while not in a party press the left d-pad and hold it for a moment. If none of these work chat may be bugged for you, its happened a handful of times to some people I know.
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Do I need to be in menu in orbit or in a game? Not sure where it is I hold left on dpad
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Try orbit or in a strike or crucible game.