From speaking with the gen surg program director at my school, competititve programs will wonder why you don't have a letter from the chairman of your general surgery dept. I have found programs that don't require a chairman letter, but they might question your reasons for applying to g-surg without any g-surg people recommending you. But you can only do what you can. If you don't have anyone from g-surg who will write you a letter, go for it and be prepared to do some explaining in interviews.
