Lighting is one of the most over looked aspects of keeping chameleons with live plants. Plants need light. Different plants need different levels of light intensity.
Typical "plant" floros you find at DIY stores and Wilmar/Target are better than standard floro tubes but are usually on the high end of the spectrum, outside of what's "ideal" for plants. For that you want a bulb in the 5500-6700 Kelvin range. Little tip...if it doesn't state it being in that range on the box, it usually isn't. You can look through plant supply websites for the right bulbs or you can go to your local pet store. They usually will have limited supply of plant bulbs in the right spectrum. You can usually find them cheaper online at bigal's.com or drfosnsmith.com.
In response to the not using a UV bulb. That form of keeping is a possibility, but it is not easy to dose the right levels of D3, especially for a young cham that is growing and will need varying levels. It is really easy to over dose and kill your cham. So with that, no it is not something even an experienced keeper should attempt long term, and it certainly isn't something a novice should attempt.