How long can a chameleon live without food?

Depends on the species and age. Chameleons under like 4-6 months shouldn't be left without food for more than a day, adults may be fine for like 2 days probably as long as they have access to water, also species which live in harsher conditions (e.g. veileds) could survive for a longer period but still I wouldn't leave a chameleon without food for more than a day especially if it's not fully grown.