In this paper, we propose and study the parity-constrained k-supplier (PAR k-supplier) problem, generalizing the classical (unconstrained) k-supplier problem. In the PAR k-supplier problem, we are given a set of facilities and a set of clients in a metric space with distances. An integer k is also given. Each facility is associated with an odd or even parity requirement. The goal is to open at most k facilities and assign each client to an opened facility, such that the number of clients assigned to a facility meets its parity requirement, and the maximum distance of any client to its assigned facility is minimized. As our main contribution, we provide a constant-factor approximation algorithm for the PAR k-supplier problem with a ratio of 9. Our algorithm proceeds by first ignoring all parity requirements and constructing an (unconstrained) k-supplier instance. Next, we design an algorithm to solve the constructed instance and obtain a solution that may have some invalid facilities. An invalid facility is an opened facility whose parity requirement is violated. Last, to obtain a feasible solution, we match up all the invalid facilities and make reassignments according to each invalid pair.