The cross section at 90\ifmmode^\circ\else\textdegree\fi{} (lab) for elastic scattering of protons by ${\mathrm{He}}^{3}$ has been measured from ${E}_{p}=0.125$ MeV to above 1 MeV. No significant departure of the $s$-wave phase shifts from the hard-sphere value is seen. Experimental upper limits for the dimensionless reduced width of a $J={0}^{+}$ state vary from 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ at the lowest energy to ${10}^{\ensuremath{-}4}$ at 1 MeV, and lead to the assignment of $T=0$ to the ${0}^{+}$ state at 20 MeV in ${\mathrm{He}}^{4}$.