Can I study while in H-1B status?

Yes. As long as you maintain your status and continue your employment as described in your H-1B petition, you may enroll in full-time or part-time, degree or non-degree program. However, note that you may not be able to complete all components (e.g. required teaching in a PhD program) of a program while in H-1B status, due to specific requirements of the program. You should discuss this with an international student advisor at the institution where you intend to enroll.