Hey Jim,
In a nutshell... It is legal to catch Chuckwallas and like everything there is a limit to both how many you can catch per day (like fish), and keep in captivity. The last that I read.. you are legally allowed to catch 2 per day, and keep a total of 12 Chuckwallas that are native to California. Native Chuckwallas are listed as **Vulnerable** and are currently not protected. It is against the law to release Chuckwallas, or any other native or non-native reptile/animal into the wild even if you caught them. This is to protect the wild populations from foreign diseases and viruses... It also protects other species that may feed on them from these things as well.
I am not sure if you are allowed to use things like nooses to catch reptiles. I've always caught Chucks by hand. Certain "tools" may be considered tools for poaching or trapping.
Look into "bag and possession" laws for the state you plan to collect Chucks, or D. Igs. I found the following by just typing in California, bag and possession laws... I've been told that all you need is a state fishing license, but I would look into it more and not take any chances. I've always used a fishing license clipped to my shirt or shorts while out "herping". What throws me off here is that it always says **permit** not **license**.
http://www.dfg.ca.gov/licensing/pdffiles/fg1502.pdf
I hope this helps, and I'm sure there are people here that know much more than I do about this stuff.
Good luck.
-Kory