Yes. You may evict a tenant who is participating in the Housing Choice Voucher Program, so long as you provide proper legal notice. You must also provide the PHA with a copy of the initial eviction notice once the process has been started. In order to evict a tenant, you must abide by all local and state eviction laws. Legal reasons for eviction include failure to pay rent, causing damage beyond normal wear and tear, and illegal use of the unit.