Yes, Section 8 Housing Choice Voucher participants may move their voucher to a different area, but only once specific conditions are met. This process is referred to as "porting."
A Housing Choice Voucher participant may only port their voucher after one year of residency in the jurisdiction of the housing authority that issued the voucher. If the voucher holder was a resident when they initially applied for the voucher, they may request to move to a different jurisdiction at any time. (For example, if you live in New York City, New York, and apply for the Chicago Housing Authority Section 8 waiting list in Illinois, you must live within the Chicago Housing Authority's jurisdiction with your voucher for 12 months before porting. But, if you live in Chicago, IL and apply for the Chicago Housing Authority Section 8 waiting list, you may port to a new area any time after you receive your voucher.)
Housing authorities are given a lot of leeway by HUD in their porting policy, so there may be other specific factors required to be able to port your voucher.
To begin this process, you must first contact the housing authority that currently manages your voucher. You will then be instructed to contact the housing authority that serves the area you are interested in moving to. That housing authority must either be "absorbing" or "billing" vouchers. Absorbing means that the housing authority takes full control over your voucher. Billing means that the housing authority will take you in as a resident, but it will bill your previous housing authority for its share of your monthly rent.
If the housing authority is not either absorbing or billing, you cannot port to that housing authority. Continue contacting other nearby housing authorities until you find one that is either absorbing or billing vouchers.
It is important to consider any expenses involved in moving to a new location such as your current lease, rental deposit, moving and travel costs, and utility costs. Have a plan for transportation, school registration, employment, and childcare before you start the porting process to ease the transition to a new home.