They can go without food, if they have to, for quite awhile. A couple weeks even. However I would not recommend leaving it unfed for more than a week.
WATER MUST BE PROVIDED EVERY DAY.
You've taken on the responsibility of being a pet owner, thus you MUST find someone to care for your animal while you are away - or dont go.
It's not the food that is going to be an issue, it's going to be the water. They don't just drink from water bowls, they need misting or a dripper. Also if you leave a large amount of food in the cage the chame will most likely eat it all in the frst day or two since they are pigs. Personally I would never leave my house for over 48hrs. without having some care for my chams. Even when I'm working from 5am-5pm I have my girlfriend come over and take care of them. But I guess it is different for everybody. I think of it this way, how long do you think you could sit in a cage without food, proper water supply, or other necessities for? It's just a thought...
Also how will it be provided with light and the proper temperatures and everything? You really need to find someone to watch it or I could easily see something going wrong with this situation.
Where do you live? Maybe there's a Forums member close to you that could care for your cham. If no member close by then you need to find a friend or neighbor.