Enrichment for chams is an interesting idea, it is one of the things I try to look for in my observations.
It is interesting, because if we observe their basic behavior, they pretty much seem to bask at their favorite, or likely only spot, depending on how we choose to feed, they may get excited at the site of a food dish, or like mine seem to recognize the tub I keep the roaches in and come down to get some.
The rest of the time seems to vary by sex.
Males are food driven, but they ,or at least mine does show curiosity is far more likely to venture out and explore. His enclosure remains the same, but if I change around things around in the room there is always the same reaction. He must try to get to any newly accessible area that is above his normal perching height. This often spurs the "exploring" behavior, where if the door to the room is left open he will venture out.
So first he claims his new territory and the searches for a mate. On this behavior to create enrichment you could ,as mentioned, make a free range "tree" just use a large plastic pot, use a long branch stuck in the center for the tree part. Them periodically move it to a new "High Ground" Keeping his cage, safe zone, stable.
For the female it seems different, she not as exploratory, and their goal seems too be more just about food. The only time she ventures out is if she sees something to eat. They will venture when looking for a place to lay eggs, but that is different. For her I always hand feed, you can use a hand held cup if you don't like bugs, I feed her from different areas and often make her climb a ways to get it. As a result she appears very tame. It is all about wanting food, but she will follow me, she will climb on to me ,but no touching. If I hold a palm out she comes. So basically use food to get them to climb, stretch, and hang to get food.
