Trials and Tribble-ations - S5-E6
Corrected entry: When Kirk comes onto the bridge, and discovers the Tribble in his chair, he sits down, and hits the Comm button to call McCoy. It makes a sound that signifies the channel's open. In the original shot in TOS, the button only clicked, with no extra sound added.
Correction: O'Brien is posing as an engineer in this timeline. He could have been called upon to actually fix something, freeing up an engineer that wasn't available in the original timeline to fix a low-priority problem like the Captain's bridge comms not beeping right.
Captain Defenestrator