Our office hours are from 8:00 a.m. - 4:00 p.m. Two (out of three) of us work earlier hours in the event technical support is needed. Our supervisor wants one of us to work 8:30 - 4:30 and have us decide which one will change their work hours. None of us want to change our current hours. Is this something he can do?

Sure - he can set working hours as needed to satisfy company needs.

It's nice that he has given you the opportunity to decide among yourselves, rather than dictate who shall work the 8:30 - 4:30 shift. You might agree among yourselves to do a rotating schedule, where each of you works that shift 1 out of 3 weeks. If you can't agree to that then you can expect the boss to make a unilateral decision.

Sometimes a change in job requirements means that the employee is entitled to unemployment, even if they quit.
This is not a big enough change, I'm pretty sure.
You could check with your local unemployment office.

If the change of 30 minutes means a lot of added traffic getting to and from work, then I would tell that (all 3 of you) to the employer, and say that you think it's worth a small raise.
If that doesn't work, I think ebaines idea is best. Maybe best anyway. I have a feeling a raise isn't in the cards.

I would add that my comment is geared towards US employers. If the OP is in another country then local laws may be more restrictive about changing work hours.

Bosses can make changes to workers hours if they deem it necessary, and he has given you three a choice. He didn't have too, in my opinion.

In most places, he can just tell you that your hours have changed, this may be restricted by union agreements or employee contracts.

He never had to give you a choice. He could have just picked one.