This is a 24 week double-blind study in which subjects will be randomized 2:1 to receive Xolair (Omalizumab) or placebo. 14 subjects will receive Xolair and 7 will receive placebo. Xolair injections will occur every 2-4 weeks. Aspirin desensitization will occur several weeks later. One month after desensitization, the final visit will occur in the GCRC.