Chrysler Group LLC on Monday reported a $690 million loss for its first quarter on expenses related to a debt payment and a charge-to-earnings stemming from its purchase by Italy’s Fiat SpA in January.

The Auburn Hills, Mich., auto maker is owned by Fiat but still releases its profit and sales separately as a result of debt requirements. It posted a net profit of $166 million in the same year-ago period. Revenue for the quarter ended…