Crimes in Chamonix, are very low, just use common sense such as locking rooms, not walking around with large amounts of money and not leaving your personal belongings unattended.
Like other tourist areas, in high seasons the pickpockets also come to town. Also if you have an expensive mountain bike or skis, be sure to keep an eye on them and lock them up when you can’t watch them.
Recommend avoiding using the currency exchanges and cash machines in the open air in town centre – pickpockets seem to hang out here ‘targeting’ their victims (they have a very good view from several spots where they can easily hang out and look like tourists).