Plans have been submitted for work at the Grade I Listed Hospital of St John Baptist without the Barrs in Lichfield, where a chimney stack is in danger of collapse.
The distinctive building on St John Street features eight chimneys along its front which date back to the 15th century, when it served as an almshouse.
It now houses accommodation for the elderly and also features a chapel.
A planning statement submitted to Lichfield Council says the historic building's southernmost chimney has a "concerning" leaning angle.
It says: "Whilst the chimney has been in this situation of leaning for many years, it is considered that the lean is creeping.
"The risk of eventual collapse towards the building interior is real, and therefore the impact would be significant for occupants and the listed asset itself."
The statement adds that the chimney in question may not have undergone repair works when some of the other stacks were rebuilt in the 20th century.
It says "positive action" is needed as soon as possible to prevent "total structural failure", adding that the risk of collapse is "too significant to ignore".
The proposals will see the chimney taken down to roof level, with as many bricks as possible restored to be used in the rebuild.
It says in the statement: "It is hoped that at least 60 per cent of the existing stack bricks will be reclaimed.
"An allowance of 40 per cent is anticipated for using another salvage brick sourced to match size, colour and appearance."
The statement concludes: "The proposals will repair the building to avert disaster and ensure the risk of collapse is arrested.
"The building itself will benefit from repair and the aversion of the risk of collateral damage to the grade I building fabric."