  We present a comparison of the strong couplings of light ($u$,~$d$,~and~$s$),
$c$, and $b$ quarks determined from multijet rates in flavor-tagged samples of
hadronic $Z^0$ decays recorded with the SLC Large Detector at the SLAC Linear
Collider. Flavor separation on the basis of lifetime and decay multiplicity
differences among hadrons containing light, $c$, and $b$ quarks was made using
the SLD precision tracking system. We find:
  $\alpha_s^{uds}/{\alpha_s^{\rm all}} = 0.987 \pm 0.027({\rm stat}) \pm
0.022({\rm syst}) \pm 0.022({\rm theory})$,
  $\alpha_s^c/{\alpha_s^{\rm all}} = 1.012 \pm 0.104 \pm 0.102 \pm 0.096$, and
$\alpha_s^b/{\alpha_s^{\rm all}} = 1.026 \pm 0.041 \pm 0.041\pm 0.030.$
