I have a paper selected in a very prestigious conference in our field. Is it appropriate if I ask the contact person that I am interested in chairing any conference session? Note that I am a Ph.D. student as of now and not a faculty member or qualified Ph.D. doctor.
Yes, it's okay to volunteer to chair a session, but there is not a lot of benefit to it and you might be turned down. People may see it as unusual, since it's not a prestigious job (certainly nothing to list on your CV).
It's important to have a chair who can keep the session running on time, provide appropriate introductions, and sometimes ask a question if there are no questions forthcoming from the audience. These are fairly easy tasks, but if I was organizing the conference and I didn't know you, I probably wouldn't agree to let you chair since I don't know how capable you are in these regards.
You need to be able to stand up and stop big shots from talking if they exceed their time. I have seen chairs turning the mic off for people overrunning their time. Do you want to be the one shutting up some big guy?
Plus, you should think of questions to ask for every talk in your session, to avoid silent embarrassment after the talk if nobody else asks questions. There are cool talks where this is easy, but for some tedious ones this can be like squeezing blood from a stone.
I should say, it's a bit like in the army: if you are asked to chair, do it without making a fuss, but don't volunteer...