No, they have no chance.
Arsenal always bottle it, and there's no reason to think otherwise now. Their recent performance against Southampton was disgraceful, they choked plain and simple. Nacho Monreal (his name sounds like Set Menu No. 2 at my local Mexican restaurant) was particularly poor and is clearly a weak link in the side. All of Arsenal's usual failings were on display, they looked small, slow and physically weak compared to Southampton's bigger, seemingly more athletic players. They missed chances (Giroud and Walcott are particularly bad at that) and they gave the ball away too often.
Another reason why they can't win the title is injuries. Arsenal's injury record has been so bad for so long now that there must be something Wenger is doing wrong, either with the training or match preparation. No team can be that unlucky. Tomas Rosicky has spent more time on the injury list than Gary Glitter has spent on the sex offender's list; Jack Wilshire isn't much better either. But the big ones are Sanchez, Cazorla and Coquilin; with them still injured for much longer Arsenal have no hope.
Yes, they can do
There is plenty of counter-evidence, however, that Arsenal can win the title. For starters they have Mezut Ozil. He may have the looks of someone who's just been punched repeatedly in the face by Brock Lesnar, but boy what a player. His recent performance against Bournemouth was absolutely exceptional and with 16 league assists already this season he is more than on course to be Thierry Henry's all-time Premier League record of 20. Ozil is a joy to watch and has a great chance of winning Player of the Year, especially if Arsenal do go on to win the Premier League title.
The other reason that Arsenal have a great chance is that their rivals don't look up to much, quite frankly. Chelsea and Manchester United's problems are well documented and Manchester City have an oddly Arsenal-like injury list. City are also far too dependent on Kompany in defence and Aguero to score the goals, Arsenal however have far greater strength-in-depth and this may well count in their favour in the long run.
Can Arsenal do it? I think there are good arguments on both sides. It will be interesting to find out.