Because I couldn't view the back of this photo, I conducted various copyright searches on the UPenn site to try determining if any copyrights had been registered.
I searched the complete volumes for film and artwork for the years 1965 to 1969. Desilu Productions registered only w:The Lucy Show and w:Yours, Mine and Ours (1968 film) in conjunction with Walden Films. NBC registered only one still image-a color slide from Bonanza of Ben Cartwright on a horse.
Nothing turned up when I searched Star Trek for the years 1965 through 1969 in either film or artwork.
There's no evidence of copyright for this time frame from either production company.
Legal disclaimer This image shows (or resembles) a symbol that was used by the National Socialist (NSDAP/Nazi) government of Germany or an organization closely associated to it, or another party which has been banned by the Federal Constitutional Court of Germany.
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (50 p.m.a.), Mainland China (50 p.m.a., not Hong Kong or Macao), Germany (70 p.m.a.), Mexico (100 p.m.a.), Switzerland (70 p.m.a.), and other countries with individual treaties.