Eddy said dealers get $20 for each customer who activates a credit card, which he said basically covers the cost of processing the applications.
In addition, F&I managers and others who sign up customers are entered in contests for prizes, Chrysler spokesman Ralph Kisiel said.
Customers can apply for the Chrysler Group MasterCard beginning in May. A campaign with dealership displays, direct mail and online promotions starts June 1 and runs through August, the company said.
Each Chrysler Group brand gets its own card. Chrysler, Dodge, Jeep, Ram and Fiat customers earn three points for every $1 spent at participating dealerships; two points for every $1 on travel-related purchases; and one point for each $1 spent on all other purchases, the company said.
Dealership employee prizes include eight trips to the Major League Baseball playoffs, prepaid credit cards worth $1,000, and iPads, Kisiel said.
Customers can redeem their points when buying a vehicle or purchasing parts and service. They can also choose standard rewards outside the Chrysler Group, such as gift cards and travel, anywhere MasterCard is accepted.
Chrysler's former captive finance company, Chrysler Financial Services -- now TD Auto Finance -- offered a credit card from 2005 to 2009. Chrysler switched its preferred-lender relationship to GMAC -- now Ally -- in 2009.
The new card is offered through the Chrysler Group, First National Bank of Omaha and MasterCard.