Private tours of the Vatican

To avoid confusion, the Sistine Chapel is part of the Vatican Museums. You have to walk all the way through the Museums to reach the Chapel. Tickets to the Museums sell out well in advance, so you'll need to be very clear with your guide as to whether you or s/he is buying the tickets.

St. Peter's has a separate entry process which involves a very long (though reportedly fast-moving) security line. It is now possible to prebook an entry time for St. Peter's that includes an audio guide. That gets you into a dedicated, much shorter security line. This is a highly recommended approach. There's quite a long walk between the door to the Vatican Museums and the door to St. Peter's.

There used to be some tour companies offering combination tours of the Vatican Museums and St. Peter's that often (not 100% of the time) were allowed to take their clients through the door connecting the Sistine Chapel to St. Peter's. That avoided the long walk between the Museums and St. Peter's. I don't know whether that option still exists.

Be very careful to select a reliable tour company. It will be very awkward if your company cancels the tour shortly before it is due to happen, because at that point online tickets to the Vatican Museums will be sold out. If that happens, you will be stuck in a very long line--a line that does not move fast.

I'm sorry that I cannot help by recommending a tour company or guide. I did the Vatican Museums on my own.

I highly recommend local company Miles&Miles (as recommended by Rick Steves). We booked two private tours with them, including one to the Vatican. Many of our friends have now used them as well. They take care of everything for a wonderfully seamless experience!

My family has taken tours with Context Travel numerous times for the Vatican (museum, Sistine Chapel and Basilica) and they have very knowledgeable expert guides and tours of 6 or less people (or fully private for your group only). Check their website for tour lengths and options.

Go early. First group in the door for the Vatican Museum (Sistine Chapel). It's a mad-house later in the day.