Light Quark Masses with an $O(a)$-Improved Action

We present the recent Fermilab calculations of the masses of the light quarks, using a tadpole-improved Sheikholeslami-Wohlert (SW) fermion action. Various sources of systematic errors are studied. Our final result for the average light quark mass in the quenched approximation evaluated in the $\overline{MS}$ scheme is $m_q(\mu=2 GeV;n_f=0) = (m_u+m_d)/2 = 3.6 \pm 0.6$ MeV.