Jude Law is spearheading a campaign to raise £2.5m to rebuild the Young Vic theatre.
Jude Law is patron of the Young Vic theatre
If the breeze block building, built in 1970 as a temporary structure, is not renovated, the theatre in central London will be forced to close.
The redevelopment will cost £12.5m, £5m of which has already been met through donations and grants.
Another £5m is expected to come from lottery money later this month, so £2.5m is needed from the public.
Law, who is the theatre's patron, said on Tuesday he would be donating money himself, but refused to say how much.
The Oscar-nominated actor grew up in south London and visited the Young Vic as a schoolboy.
He said: "I remember coming here 15 years ago to see a production of Othello and being so moved at the experience of being in such close proximity to the actors.
"It was a really important part of the dream that I had to become an actor.
"To see a performance of such extraordinary theatre so close at hand taught me how enjoyable it could be, not only to be an audience member but to be a performer."
The 32-year-old star of Cold Mountain and The Talented Mr Ripley has since appeared on stage at the Young Vic twice, most recently in 2002 in a production of Marlowe's Dr Faustus.
Venue to double size
He said: "The South Bank is where theatre really started in this country. It is where people came to see the plays of Shakespeare and Marlowe, and it seems apt that the ghosts of the past should be housed here.
"The Young Vic has been here for 34 years and anything we can do to make it go on another 34, 64 or 94 years is important."
Law hopes to appear in the first production staged at the theatre when rebuilding work is finished in the summer of 2006.
Through the renovation the venue will double in size.
An old butcher's shop which once stood on the site is incorporated into the foyer and will be retained, although the area will be expanded.
The plans also include improving the main auditorium and an intermediate theatre built, along with extra workshop, office and backstage space.