They'll find it really difficult because they haven't won anything for 6/7 years and the habit is a hard one to break. Arsene Wenger's team over that time has done very good things up to a certain point but then they seem to run out of steam at the last hurdle.
The big test will come when the Champions League starts to get serious. With Walcott out Wenger will have to adjust his squad accordingly or else he'll find himself out of both Champions League and Premier League.
Personally I'd love to see him win the Premier League. I don't like the way Chelsea as a club operate, bringing in different managers every other year just on the whim of Abramovitch. I think English football needs more stability when it comes to ownership. Arsenal run their club with decent values, remaining loyal to a man who has brought great status to Arsenal.
Manchester City are favourites I think, with a strong defence and incredible attacking ability.
Liverpool are dark horses but will need some luck to win the Premier League this year.