Never more than once a week and only to give them sun and clean cages. Chameleons should NOT be handled, they are a hands-off pet. While many people here will tell you "oh my cham loves to be handled", they are delusional... handling a cham will subject it to unnescesary stress so if you care about your animal, simply don't do it.
Now, this is a good rule to go by, but it is not always 100% true.
I reccomend that people handle their chameleons regularly for a few reasons:
1.More frequent handling will acclimate the chameleon to it, making it non-stressful in many cases.
2.A chameleon that is somewhat used to handling will be much less stressed when handling is 100% necessary.
3.if you do not handle them, it's hard to inspect them for injuries, bne problems, sickness, etc.
4.When your chameleon NEEDS to be handled, it's going tobe much less stressful on it (and you) if the animal is used to handling. And if the chameleon is sick, the less stressful the situation the better.
Handling a mean chameleon, like a male veiled, can be tricky. It will take months, or years to acclimate them to handling -but it does not have to be stressful to them.
NEVER grab them, unless it's absolutly necessary - they hate that, an dit's not going to make them use dto handling. You have to coax them onto your hand with food. They need to hand feed for this to work. My big male was EVIL for over a year. When he started to hand feed (around 18 months, I think) I was able to get him to climb onto my right hand by luring him out onto it with a bug in my left hand. Now,if I do that, he'll sit on my hand unstressed. I can even feed him with one hand as he is perched on the other.
It was important that I did this, as he had a bad injury that needed attention. I was able to apply antiseptic to him without grabbing him - which woudl stress him out.
Handling them doesn't have to be stressful if you do it right.
furthermore, there are friendly chameleons. Seriously. Melleri are especially known for being outgoing. My CB melleri will climb TO me if I have her cage open - even if I'm not feeding her. I just stick my hand out, and she climbs right on, holding on with gentle pressue (WC's are not gentle!).
If you want a pet that you can handle, and pet - get a bearded dragon, not a chameleon. Chameleons can be handled, and most can be trained to be handled regularly, and stress free, with time and practice. If you do not handle yor chameleon - which is fine - the times you DO handle them will be stressful. I try to reccomend people get their chameleons use dot it, so they are confident in handling the animal in case they really need to handle them.
At the last reptile show, I met 2 differe people that lost their chameleons because they were afraid to take it out and to the vet!
I handle My Veiled 1-2 times a week. For maximum 5 mins. It is for the same reason Eric said. Most of the time I take him out of the cage, set him on a plant, Do maintenance on his cage, then put him back in. I also hand feed him about 1-2 times a week for the trust issue. So far so good.
LOL. It is the old addage of how we place comma's and how it changes sentence structure. For example:
1) I handle him roughly two or three times a week...
2) I handle him roughly, two or three times a week...
Play on sentences can be amusing.
See the difference? Changes the whole scope of the meaning of the sentence.
As far as handling chameleons, I find each chameleon has their own unique personalities. I have some that just love attention and love to be hanging out with me and completely without stress. Others however, don't like to be handled at all. It is best to err on the side of caution as stress is not a good thing for chameleons and it is best to understand that they are not like a cat or dog. They feel safer in their own habitats, and it is best to understand in the beginning that chameleons are not to be handled as a rule of thumb, yet I agree with Eric here too. It is important to try to earn the trust of your chameleon so that he feels comfortable with you and when he does need to be handled, he is not stressed by doing so.
So I believe both Eric and LowandFrequency are correct. With all my chameleon breeders, there is not one that gets upset when I handle them. They know me, trust me, and understand I mean them no harm. But, I also work with them constantly 7 days a week, as it is my job. I also have Giant Monkey Tailed Fischers, Deremensis, Quadricornis, among other montane species who are very relaxed as well. My Peacock Perreti I don't handle at all and let them do their own thing in their habitat, as they are very shy chameleons and can be very easily stressed.
Having said this... don't ever, ever believe that they are able to be handled like other pets. They prefer solitude, moderation in handling, and at times, depending on the chameleon personality, handled ONLY when necessary. Use common sense. You can tell if your chameleon is stressed when you try to handle him. If he is showing stressful behaviors? Back off. Take much time with them at little increments of time. Always, ALWAYS, approach your chameleon with him being higher than your head and bring your hand slowly upwards towards under their chin for them to grasp their feet onto your hands if they are receptive to being handled. Never grab a chameleon by it's back... they view this as an aggressive move, as in the wild they are are prey and predators will approach them or grab them in this way. Let them see you... be slow in your approach... go towards them, palm up with your index finger and middle finger spread apart (like a peace sign) for them to use as a way to walk onto your hand.
So, in closing... Chameleons are NOT pets like cats and dogs and prefer to not be handled. They DON'T like to be petted. Yet, it is possible to slowly work with them and through time they will get used to your handling with less stress when it is necessary to handle them. In doing so, you cause less stress for them when you must take them to the vet, give them medications, clean their cage, or even take them out to enjoy a change of scenery by placing them on a tree for a short break of their caging.