We present the first detailed abundance analysis of the metal-poor giant HKII 17435-00532. This star was observed as part of the University of Texas long-term project Chemical Abundances of Stars in the Halo (CASH). A spectrum was obtained with the High Resolution Spectrograph (HRS) on the Hobby-Eberly Telescope with a resolving power of R~15,000. Our analysis reveals that this star may be located on the red giant branch, red horizontal branch, or early asymptotic giant branch. We find that this metal-poor ([Fe/H]=-2.2) star has an unusually high lithium abundance [logɛ(Li)=+2.1], mild carbon ([C/Fe]=+0.7) and sodium ([Na/Fe]=+0.6) enhancement, as well as enhancement of both s-process ([Ba/Fe]=+0.8) and r-process ([Eu/Fe]=+0.5) material. The high Li abundance can be explained by self-enrichment through extra mixing that connects the convective envelope with the outer regions of the H-burning shell. If so, HKII 17435-00532 is the most metal-poor star in which this short-lived phase of Li enrichment has been observed. The Na and n-capture enrichment can be explained by mass transfer from a companion that passed through the thermally pulsing AGB phase of evolution with only a small initial enrichment of r-process material present in the birth cloud. Despite the current nondetection of radial velocity variations (over ~180 days), it is possible that HKII 17435-00532 is in a long-period or highly inclined binary system, similar to other stars with similar n-capture enrichment patterns. Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.