The chemical abundances of planet-hosting stars offer a glimpse into the composition of planet-forming environments. To further understand this connection, we make the first ever measurement of the correlation between planet occurrence and chemical abundances for ten different elements (C, Mg, Al, Si, S, K, Ca, Mn, Fe, and Ni). Leveraging data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and Gaia to derive precise stellar parameters ({sigma}_R_*~2.3%, {sigma}_M_*~4.5%) for a sample of 1018 Kepler Objects of Interest, we construct a sample of well-vetted Kepler planets with precisely measured radii ({sigma}_R_p~3.4%). After controlling for biases in the Kepler detection pipeline and the selection function of the APOGEE survey, we characterize the relationship between planet occurrence and chemical abundance as the number density of nuclei of each element in a star's photosphere raised to a power, {beta}. varies by planet type, but is consistent within our uncertainties across all ten elements. For hot planets (P=1-10days), an enhancement in any element of 0.1dex corresponds to an increased occurrence of ~20% for super-Earths (Rp=1-1.9R{Earth}) and ~60% for sub-Neptunes (Rp=1.9-4R{Earth}). Trends are weaker for warm (P=10-100days) planets of all sizes and for all elements, with the potential exception of sub-Saturns (Rp=4-8R{Earth}). Finally, we conclude this work with a caution to interpreting trends between planet occurrence and stellar age due to degeneracies caused by Galactic chemical evolution and make predictions for planet occurrence rates in nearby open clusters to facilitate demographics studies of young planetary systems.