In reply to GStone:
I've only ever camped at 'Camping du glacier d'Argentière' in Les Chosalets so can't compare with any in Chamonix- it's a fantastic campsite and often busy. This isn't necessarily a problem but also completely depends what you're looking for. Generally, it is filled with climbers so is also a good place to meet partners.
No issues with just turning up in the dead of night. The barrier will be shut after 10pm but parking is available very close. Just speak to the owners in the morning.
Obviously, if it's not for you, you could always move on to Cham the following day.