As chaplain of the 4077th, Father Mulcahy got his own tent which gave him a private space to tend to the spiritual needs of the camp personnel. Like the other accommodation tents in the camp, it is a "Tent GP small", one of several under a camouflage net in a line between the large mess tent and the motor pool/stable area. According to a hand drawn map in the souvenir booklet "M*A*S*H Bind Up the Wounds" published by the Smithsonian Institution for the exhibition of the same name, the Chaplain's tent is the first one after the motor pool, directly opposite the Officers' Club.
The red arrow shows the location of the Chaplain's tent according to the map in the Smithsonian brochure "M*A*S*H Binding Up the Wounds", an exhibition about the TV series. In reality, there were fewer accommodation tents on the exterior set than were needed so many of the tents did double duty.
The inside of the tent is simply furnished, with a bed, a stove for heat, a desk (often covered with a red table cloth), and chairs - although the arrangement of the furniture changes between seasons. Outside, Mulcahy maintains a simple garden.
The Chaplain's tent features significantly in a number of episodes as a place where confessionals are conducted and advice is given to various camp personnel and there are many good views of the inside. In "Dear Dad...Again" (Season 1), Captain Casey confesses that he is not really a doctor. Similarly, in "Tea and Empathy" (Season 6), Corporal Benny Bryant confesses that he has stolen cases of penicillin and hidden it under a bell in an abandoned school house. In "Morale Victory" (Season 8) Winchester is crushed and seeks Mulcahy's advice when he is unable to reach out to a concert pianist soldier who has injured his hand. In "Letters" (Season 9), it is Hawkeye's turn to seek advice in the chaplain's tent when he does not know how to reply to a schoolboy's letter accusing him of fixing up wounded soldiers only to have them sent out to be shot again. This episodes has particularly fine wide angle views of the inside of the tent.
Mulcahy tending to his garden outside his tent. Scene from "Dead Dad...Again".
Corporal Benny Bryant confesses to Mulcahy in "Tea and Empathy". The stove is clearly seen.
Probably the best wide angle view of the inside of the tent is found in this scene from "Letters". The bed, desk and chairs can be seen but not the stove. The stove would typically be in the center of the tent, about where the camera is.