The United Auto Workers trust owns 41.5 per cent of Chrysler's shares. Italian carmaker Fiat owns the rest.
The trust wants the company to sell 16.6 per cent of Chrysler stock owned by the trust.
Fiat and the trust are fighting in court over the value of Chrysler shares. Fiat has options to buy up to 16.6 per cent of the trust's shares. It has filed plans to buy 6.6 per cent and says it wants to buy the rest.
Fiat and the trust got their shares after the U.S. government bailed out Chrysler in 2009.
The request is the first step toward a public sale that could take many months.