WMG / Star Trek S2 E18 "The Immunity Syndrome"

Kirk and Uhura are pretty obviously shown to be romantically close.

In the early fanzine T-Negative 23, July 1974, Mary Louise Dodge (who was already well known for Shipping those two lavishly — she later wrote some lush romance Fan Fic about them) had her Shipping Goggles firmly in place for this episode. She said: "... as they are all being drained of energy, he stops and rubs her back rather absently, and touches her several times, comfortingly, as he moves back and forth on the bridge. These are small intimate gestures born of long association and intimacy."