How is it possible that my boyfreind was positive for chlamydia and I am negative?

A few possibilities. 1. Most likely explanation. He has it and has not given it to you yet. 2. You both have it but your test did not detect it. This is called a false negative. 3. Neither have it and his test was incorrect. This is called a false positive. Option 1 is by far the most likely. You both should be treated.
STD. Well, it appears he probably did not get the infection from you. Fortunately, you did not test positive, however, you should not have intercourse with him until he completes his treatment. If you have had unprotected intercourse with him since his diagnosis, you might be safe to get rechecked.