Unilever PLC is rolling out its popular Magnum ice cream bars in the U.S. for the first time, mounting a fierce challenge to big-name incumbents—Mars Inc.'s Dove bars and Nestlé SA's Haagen Dazs bars.

Magnum bars—premium ice cream on a stick wrapped in a thick chocolate shell—were launched in the U.K. in 1987 and have become the world's top individual frozen dairy snack, accounting for 6.8% of the global market in 2009, according to Euromonitor International.

Despite...