Seismic anisotropy, measured through shear wave splitting (SWS) analysis, can be indicative of the state of stress in Earth's crust. Changes in SWS at Kīlauea Volcano, Hawai‘i, associated with the onset of summit eruptive activity in 2008 hint at the potential of the technique for tracking volcanic activity. To use SWS observations as a monitoring tool, however, it is important to understand the cause of seismic anisotropy at the volcano throughout the eruptive cycle. To address this need, we analyzed SWS results from across Kīlauea in combination with macroscopic surface structures (mapped fractures, faults, and fissures) and stress orientations inferred from fault plane solutions. Seismic anisotropy seems to be due to pervasive aligned structures in most regions of the volcano. The upper East and Southwest Rift Zones, however, show a bimodality in stress and SWS, suggesting a stress discontinuity with depth, perhaps related to magma conduits that trend obliquely to the dominant structure. Other areas in and around Kīlauea Caldera display principal stresses of similar magnitudes, indicating that small stress perturbations can rotate the maximum horizontal compressive stress direction by up to 90^°. In these locations, static structures generally control SWS, but dynamic conditions due to magmatic activity can override the structural control. Monitoring of SWS may therefore provide important signs of impending volcanism.