Continental passengers have a new incentive to acquire a Chase credit or debit card.Effective immediately, primary Chase credit or debit cardmembers are exempt from the $15 first checked bag fee. Cardmembers checking one bag roundtrip can save $30 with the new benefit and the fee waiver is extended to passengers traveling on the same reservation and checking in at the same time as the cardmember. The Chase debit card has a $25 annual fee ($65 annual fee for the Preferred Banking card) and the TravelBank World MasterCard comes with a $29 annual fee (waived for the first year). Annual fees for other cards range between $65 and $85. So if you aren’t an elite member with Continental and want to avoid the first checked bag fee, it may be worthwhile to consider Continental’s co-branded credit or debit card. Cardmembers carrying the Presidential Plus World MasterCard will be able to check two bags at no additional cost–a savings of up to $80 roundtrip. Keep in mind that the Presidential Plus card comes with Presidents Club membership, priority airport services and Hyatt Platinum level, in addition to a hefty $375 annual fee.