Is there an annual limit on the number of H-1B aliens?

Yes. The current law limits the number to 65,000 aliens who may be issued a visa or otherwise provided H-1B status in FY2004 and to the present. Within the 65,000 visas now available annually, 20,000 must be set aside for H-1B beneficiaries who have earned a U.S. master's degree or higher.