In fact, their chances are zero.
The Web site presents a 2010 NHL playoff bracket and uses statistics in order to predict each team's chances of winning each round. The entire playoff was simulated 2,001 times using rosters and stats from the 2009-10 season, taking into account home-ice advantage.
The simulation predicts that Boston has a 20.39 percent chance of beating Buffalo in the first round, but after that, the B's have a 1.53 percent chance of winning the conference semifinals. They have a zero percent chance of winning in the conference finals and a zero percent chance of winning the Stanley Cup. (Technically, though, the only way the Bruins have a zero percent chance of winning the Stanley Cup is if they do not qualify for the playoffs, which is not the case.)
According to the simulation, the Capitals have the best chance at winning by a landslide. They are 96.78 percent certain to win their first-round matchup against Montreal, 93.25 percent certain to beat the Penguins in the conference semifinals, 70.55 percent certain to beat the Devils in the conference finals, and 50.92 percent certain to win the Stanley Cup over the Blackhawks, four games to two.
The best chance a Western Conference team has of winning it all is the Blackhawks at 12.12 percent. Top-seeded San Jose's chances are just 10.49 percent.
You can run a simulation of your own by clicking here.