Not having a degree does not nullify your chances. I have no degree, and got an H1-B and subsequently a green card. To qualify for the H1-B, I had to show 12 years of work experience (immigration equates 3 years of work to 1 year of school), and then have my work experience evaluated by a professor. The professor had to establish that my work experience left me with the same experience as someone who would have had a degree.