Is it legal for a private citizen to sell a firearm to another private citizen?

YES, as of July of 2013 all firearm sales (transfers) in Colorado must have a background check. There are some exceptions with some (not all) family members. Check with your local firearms dealer to be sure. For your own safety, you should always have a dealer do a background check on the transfer of a firearm.

See the Colorado Do’s and Don’ts, A White Paper outlining important aspects of traveling with a gun in Colorado