CHARLOTTE, North Carolina—Sonic Automotive Inc., one of the country’s largest car-dealer companies, will open a chain of preowned-vehicle stores hoping to move on the turf of used-car retailer CarMax Inc.

Sonic on Monday will announce the creation of EchoPark stores, with the first dealership opening in Denver this autumn, a few miles from a CarMax store. Like CarMax, EchoPark will provide no-pressure shopping to customers…