Previous determinations of chemical abundances of the metal-poor red giant TYC 5619-109-1, derived via high-resolution near-infrared spectra from the Apache Point Observatory Galactic Evolution Experiment survey, indicate that this star is strongly enriched in the elements N and Al. Here, we obtain and analyse high-resolution optical spectra of TYC 5619-109-1 to verify these large N and Al overabundances and to measure abundances of a wider range of chemical elements. Our analysis confirms the N- and Al-rich nature of this star, and shows that the abundances of the s-process elements are also strongly enhanced, particularly in the heavy second s-process peak elements (Ba, La, Ce, Nd). Lighter s-process elements (Y, Zr) show smaller overabundances, and the ratio of the light-to-heavy s-process elements is consistent with the 13C(α, n)16O neutron source operating in a low-metallicity environment. The lack of Tc I lines and the abundance of Nb compared to Zr indicate that this red giant is probably not a thermally pulsing asymptotic giant branch (TP-AGB) star. Mass transfer from a former s-process-rich TP-AGB companion may produce the observed overabundances, but our radial velocity analysis provides no evidence that TYC 5619-109-1 is a binary with a white dwarf companion. We suggest that TYC 5619-109-1 formed from gas already strongly enriched in s-process elements, as found in many dwarf galaxies and globular clusters. A dynamical analysis reveals that there is only a small probability that TYC 5619-109-1 is an escaped member of a globular cluster, and in this case the most likely candidate would be ω Cen.