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While it will be extremely crowded, indeed, it's a good idea to buy your tickets in advance. The Vatican Museums online ticketing can be only be done sixty days in advance at http://biglietteriamusei.vatican.va/musei/tickets/do
Before you do, check to make sure that it is open on the date you wish http://mv.vatican.va/3_EN/pages/z-Info/MV_Info_Calendario2016.html
Alternatively, you could book via a tour company. You want to make sure the they are licensed by the city of Rome, such as www.myrometours.com