The elastic scattering of protons from $^{3}\mathrm{He}$ is calculated with a microscopic, momentum space optical potential which incorporates the full spin dependence of the NN and p $^{3}\mathrm{He}$ interactions. The theory includes antisymmetrized NN amplitudes, realistic neutron and proton distributions, nucleon recoil and binding energy shifts, Lorentz invariant angle transformations, $t$ matrices with on-shell behavior from NN phase shifts, and off-shell behavior from a realistic separable potential model. Qualitative agreement is found with differential cross section and polarization data for $100<{T}_{\mathrm{p}}<1000$ MeV.