You can ask for a LOR but I don't think it would be a good one. There's a balance between the "name" of the letter writer and the "content" of the letter. Having only known you for those few hours, unless he/she just fell in love with you - in which case he/she would have offered you a spot in the program then and there - it would be very hard to get a nice personal letter out of him/her. I would ask your attending - assuming you worked with him/her more intimately for a LOR. There's nothing worse than getting a generic LOR that says something like "Student X rotated at my program for ---days and worked in the ---unit. He/she seems to have a genuine interest in PM&R and presented his/her patients well during rounds. The attending said --- about this student...." That's not as strong as a LOR from an attending commenting on your interpersonal skills, your daily diligence, your willingness to take on extra work, your wonderful bedside manner, etc....
One thing you could do is to schedule an appointment with the chair to tell him/her how much you enjoyed working with him/her and how you are very much interested in getting into his/her program. I would give specifics on why you like the program and PM&R. Also, ask him/her for advice on how to make your application stronger and how to best get through this application process. Ask questions about the program if you wish - but don't ask dumb superficial questions you can get answered in a brochure or in the program website. If he/she liked you enough, he/she'll offer to write you a letter. Even if you don't get a letter out of it, at least now he/she knows your name and face. When your application lands on his /her table, he/she'll remember you.
