In Bal Harbour, Fla., an oceanside village north of Miami Beach, a luxury mall says it wants to help tackle one of the nation’s — and Florida’s — most intractable problems: a lack of affordable housing.

It is an unexpected move for a retail temple where Gucci, Chanel and Rolex are on offer. Affordable? Here?

But in a rare instance of bipartisan agreement, the Florida Legislature passed a law last spring intended to encourage projects like the one that the owner of the mall, Bal Harbour Shops, has in mind. Called the Live Local Act, the law allows developers to bypass certain local zoning rules and to qualify for tax breaks if their projects include enough “work force housing.”

Local officials around the state, stripped of their power to say no, don’t like it. And nowhere has seen more backlash to date than little Bal Harbour.

For 40 years, the mall’s owner, Whitman Family Development, has wanted to build a hotel alongside the shopping center, on Collins Avenue, the village’s main drag. Neighbors and elected leaders repeatedly rejected the idea. But when the new housing law passed, the owner saw a way in.

The company filed an application last month to build a 20-story hotel and three residential towers with 600 units, 240 of which would be priced low enough to qualify as work force housing under the law. If the plan meets the law’s requirements, the village of about 3,100 people — where the median household income is about $86,000 a year, well above the state average — will be unable to stop it.