Magnetic nanoparticles with room temperature remanent magnetic vortices stabilized by their curvature are very intriguing due to their potential use in biomedicine. In the present study, we investigate room temperature magnetic chirality in 100 nm diameter permalloy spherical caps with 10 nm and 30 nm thicknesses. Micromagnetic OOMMF simulations predict the equilibrium spin structure for these caps to form a vortex state. We fabricate the permalloy caps by sputtering permalloy on both close-packed and sparse arrays of polystyrene nanoparticles. Magnetic force microscopy scans show a clear signature of a vortex state in close-packed caps of both 10 nm and 30 nm thicknesses. Alternating gradient magnetometry measurements of the caps are consistent with a remnant vortex state in 30 nm thick caps and a transition to an onion state followed by a vortex state in 10 nm thick caps. Out-of-plane measurements supported by micromagnetic simulations shows that an out-of-plane field can stabilize a vortex state down to a diameter of 15 nm.