There are people who cannot get game chat to work on PC. The usual symptom is that they can be heard, but cannot hear what others are saying. There are a bunch of "fixes" available for this problem on the internet, mostly reiterating what has been said elsewhere about it, but none of them offers the real cure.
So here's what I have found out. Most PC users have more than one audio output device in their system. Often the monitor functions as one if it has speakers, or the soundcard, even if they are using a USB headset.
What Destiny does when it finds more than one audio device is to output game sound on one device and chat sound on another device. I don't know which "genius" at Bungo has come up with that, but that is why you may not be able to hear what others are saying in game chat.
To fix this, go to your audio settings and explicitly disable every audio output device except the one you want to use. That way you are forcing Destiny to send all audio output to the same output device.
Problem solved.
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This worked me. Thanks!