Pinching antennas is a novel flexible-antenna technology, which can be realized by employing small dielectric particles on a waveguide. The aim of this letter is to characterize the array gain achieved by pinching-antenna systems (PASS). A closed-form upper bound on the array gain is derived by fixing the inter-antenna spacing. Asymptotic analyses of this bound are conducted by considering an infinitely large number of antennas, demonstrating the existence of an optimal number of antennas that maximizes the array gain. To approach this bound, an antenna position refinement method is introduced. The relationship between the array gain and inter-antenna spacing is further explored by incorporating the effect of mutual coupling. It is proven that there also exists an optimal inter-antenna spacing that maximizes the array gain. Numerical results demonstrate that by optimizing the number of antennas and inter-antenna spacing, PASS can achieve a significantly larger array gain than conventional-antenna systems.