Is there any way to get rid of baby fat under your chin without surgery?

You. You can use ultherapy. Ultherapy is fairly new and fda approved. It is a non-surgical, non-invasive procedure that uses high powered ultrasound waves with the body's own natural healing process to lift, tone, and tighten loose skin under the chin. We have achieved great results with this procedure.
Not really, but... If the problem is a fat excess only (and not excess loose skin), liposuction of the area under the chin and neck is one of the most straightforward plastic surgery procedures that exist. If there is a chin projection deficiency, augmentation of the chin may help as well. See a board-certified plastic or facial plastic surgeon to fully investigate your best options.
Non surgical neck. Procedures such as thermage and ulthera using radiofrequency and ultrasound technologies are used for this purpose. Other procedures on the horizon include "fat melting" injections which are currrently being evaluated by the fda.