Based on the Chuck Norris autographs that I have, I do not believe that this one is Real.
I'm adding a Picture of one of my Signatures. This is the clearest one and excellent for comparison. Notice how the C starts with Chuck, then the curve with the 2nd C going into a K with a high loop. Notice how the N starts in Norris and the N and O are separated. The N on yours also looks like a hesitation as it loops around. In your Photo, it looks like there was a pause or stop and start between the 2 R's. And the S on the end curves up. At least in all of mine. I could go letter by letter, but these are the most noticeable things. Hope this Helps in your search.
The Bruce Lee signature looks more plausible than the Norris. I do not like the Norris. I've got to live with the Lee a little more to get beyond 50/50 either way.
Yeah, somebody really messed up that Bruce Lee Autograph, by adding a questionable Chuck Norris Signature to it. Don't you agree Woody?
Things about the Bruce I am not crazy about. At first glance, as Prince sang, it's got the look. But the Bruce sig here is to what I'm seeing on definitely in person Lee's as the Norris is to what I'm used to seeing on the same. I don't like the "ruce" and I don't like the "L". It doesn't seem to work, it seems to me to be self-anachronistic, like one section from a 70s auto and another from a mid 60s. I'm not crazy about the Lee inscription (characters) under the main body of Lee's signature either. The vibe is off to me. Due to the bad Norris, and what I noted about the Lee, the piece doesn't really work for me, I'm not confident that's Lee.
The sharpie absolves a lot of the glitches, but not altogether. I favor all 3 Norris autos that Todd Johnson posted. Those appear to most closely match in-person signatures I've seen and/or owned of Norris over a fairly generous swath of time, approx. a 30 years period.