They definitely have an excellent chance, especially considering that the next three games are in Boston. If you take a look at Lakers- Celtics rivalry, you'll see that out of the 11 times they've met in the finals, Boston won nine. A key thing to consider is that the won in 2008, beating the same Lakers starting lineup that they're facing this year.
Allen is an absolute beast at scoring once he gets going (his performance last night was amazing!), and Rondo, Pierce and Garnett are also good players. The scary thing here is that Pierce and Garnett were playing badly last night and the Celtics still won. Of course, Bryant was definitely not at his best last night, so that's something worth taking into account. I can't predict the 2009-2010 champions, but I can certainly state that this will be a finals series worth watching. These two teams are evenly matched.
I think they have a chance as well. The home court advantage is something you can not discount.