
That's Show Biz (season 10, episode 1)
Sarah, one of the members of the troupe visiting the 4077th, tells Margaret and Father Mulcahy about the ballet slippers that her brother had when he was killed in combat. Mulcahy says he knows the chaplain at the 8063rd, so he offers to call and ask if he can help with finding the slippers.
Klinger reaches the 8063rd, and Father Mulcahy takes the phone to talk to... Charlie Chaplain...
(I am well aware it's not the actor; I just thought the unintentional pun was amusing.)