This chapel is a bit of a mystery to me. It is not mentioned by any of the usual 17th and 18th century historians of the Rock - in fact the only reference I can find is by the Spanish Historian Juan Ballesta Gómez in his article Gibraltar, Siglo XVII:
Capilla del Auxilio. Miraba a los baños Arabes de la Plaza de Juan Serrano.
He gives no reference but his siting of the Capilla del Auxilio in the Plaza of Juan Serrano is interesting. The narrow street to the west of the Cathedral of St Mary the Crowned - running diagonally towards the sea - is today’s Bomb House Lane originally known by its cumbersome Spanish name of "La Calle que va a la Plazuela de Juan Serrano". The Plazuela or square has no name at the time of writing and is treated as a continuation of Bomb House Lane.
During the mid 18th century the house on the east side of this square was the home of the storekeeper of the Board of Ordnance - hence the modern Bomb House name. It was on the site of the Moorish Baths which eventually became part of the Gibraltar Museum building. The properties on the north side at the very end of the lane and facing the sea would become the Nefusot Yehuda Synagogue in 1799.
Nefusot Yehuda Synagogue - the building to the right of it with the sign is probably the Bomb House - The one between the two of them behind the palm tree might just be part of what was once the chapel of ease (1830 - Frederick Leeds Edridge) (See LINK)
However, it was Colonel Thomas James’ in his History of the Herculean Straits which was published in 1771 but refers to his experiences in Gibraltar during the early 1750s (see LINK) who offered the first clue as to the possible identity of the Capilla del Auxilio:
. . . the house which was my quarters, where I lived for five years, and which was once a chapel of ease, had its whole front of two stories, built of this petrified sand, charged with variety of shells, that took a polish, and as the house was a religious one, the door and the window over it were ornamented with mouldings, etc with an inscription above the center the window. This mansion is opposite the bomb-house, where the storekeeper to the board of ordnance is quartered, which has a good garden walled in, and joins to the rampart of the line-wall
In other words James’ Chapel of Ease is almost certainly one and the same as Ballesta’s Capilla del Auxilio. Where or how Thomas picked up the name is hard to fathom. A Chapel of Ease is by definition one built to accommodate people who live some distance from their parish church and find it difficult to get it. In this case, however, the Chapel was not more than a five minutes’ walk from the front door of Gibraltar’s main parish church of St Mary the Crowned.
Local historian George Palao has suggested that it was later converted into an officers’ mess for the Royal Engineers and that by the 1970s little was left of the original building other than an entrance arch at the back.