The Harris Museum and Art Gallery is competing against galleries across the UK for an exclusive exhibition.
Museum curators want to bring Amy Sharrocks to take part in a 120-foot high fall from the top of the building.
Sharrocks is a live artist and sculptor who is interested in putting on an exhibition to do with falling.
Kidderminster, Swansea and Oldham are also trying to tempt Amy to visit them – but only one can win.
A spokeswoman for the Harris said: “Amy is particularly interested in images of falling and the Harris’ plan is to experiment with falling from the museum’s 120 foot high central hall or from a temporary staircase leading from street level to the first floor of the museum – all aided by a 007 stuntman!
“If the museum wins, the event will take place between Thursday 15 and Saturday 17 May 2014, and will be free of charge.”
You can vote for the Harris at the Culture 24 website. All votes must be cast by 8pm on Tuesday 28 January.