Moving around whilst he is asleep?
That doesn't sound normal. Are you sure his eyes weren't open? Sometimes if you have the room lights on, even though their cage is dark it's still light enough for the to see and move around.
I cant say weather or not chams dream, but if I had to put my money on it I most likely say he was probably in an uncomfortable position and moving accordingly.
Our veiled cham Chris, is quite the sound sleeper - he heads off to his "sleep spot" and is exactly in the same place/position in the AM when we get up.