Pinching-antenna systems have recently gained significant attention as a novel reconfigurable-antenna technology due to its exceptional capability of mitigating signal-propagation path loss. In this letter, we investigate the secrecy performance of a pinching-antenna system in the presence of an eavesdropper. In particular, we derive an approximate expression of the system's secrecy outage probability (SOP) with respect to the random locations of the legitimate user and eavesdropper and analyze its asymptotic behavior. Moreover, we derive a constant performance lower bound on the SOP of the considered system, i.e., $\frac{2π-1}{24}$, which is significantly lower than that of conventional fixed-position antenna systems, i.e., $0.5$. Finally, simulation results are provided to validate the correctness of our analytical results.