Concealed Carry Reciprocity Act This bill establishes a federal statutory framework to regulate the carry or possession of concealed firearms across state lines. Specifically, an individual who is eligible to carry a concealed firearm in one state may carry or possess a concealed handgun (other than a machine gun or destructive device) in another state that allows its residents to carry concealed firearms. It sets forth requirements for the lawful concealed carry across state lines. The bill preempts most state and local laws related to concealed carry and establishes a private right of action for a person adversely affected by interference with a concealed-carry right established by this bill.