The applications for matching funds were made as part of two initiatives at the Department of Energy that are designed to speed up the development and manufacturing of electric vehicles and plug-in hybrids.
Chrysler has been operating in bankruptcy since April 30.
The announcement of Chrysler's proposal came a day before a judge is expected to rule on the automaker's plans to sell its most valuable assets to a new company owned by the U.S. and Canadian governments, Chrysler's union and Italian car maker Fiat SpA.
It also came a week after U.S. President Barack Obama announced tough new fuel economy standards for automakers.
As of 2007, when Chrysler was still part of German automaker Daimler AG, the U.S. automaker had the lowest fleet mileage of any of the major automakers.
That same year the company set up its ENVI unit to develop fuel-saving vehicle technology.
Chrysler said the vehicles it aimed to develop include the Dodge Ram 1500 plug-in hybrid, the Chrysler Town & Country plug-in hybrid and the Chrysler Town & Country electric vehicle.
The plan would also include $365 million for a national demonstration fleet of more than 365 test vehicles for select customers and partners.
"This plan will accelerate our efforts to develop and manufacture electric and plug-in hybrid electric vehicles, which will reduce the amount of time it will take to get these vehicles on the road," Chrysler executive vice president for product development Frank Klegon said in a statement.
Hybrid plug-in vehicles have both a battery plus a conventional gasoline-powered engine.