I'm going to throw this suggestion into the mix because I encountered extremely long lines when I went to the Vatican Museums last month (as in 2-1/2 hour wait when we arrived about 10 minutes before opening time on a Saturday morning). Rather than go early, go late ... as late as you can. In fact, plan your entrance so you arrive about 20 minutes before the gates close. By then, the line should be fairly short and you can just walk by everything else and see the Sistine Chapel. Even on that Saturday, I exited the horrendously overcrowded museum about 10 minutes before the entrance closed and there was, literally, no line. But you really have to keep on top of when the museum closes. A group of people arrived right after they closed the doors and were denied admission.

Otherwise, taking a guided tour to avoid the lines is the best strategy. It's your choice, but I don't think you need to do that.

But I'd also urge you to see something other than the Sistine Chapel. It's somewhat less than overwhelming, even with the beautiful paintings; and there are a lot of other great things to see in the Vatican Museums, but you can still keep your visit to an hour. And do take time to walk around St. Peter's. The lines there aren't horribly long and move quickly, and the interior of the basilica is breathtaking.