  We present preliminary results of the calculation of the positive-parity
ground state charm baryon spectrum using of N_f=2+1+1$ dynamical quarks. The
calculation uses a relativistic heavy-quark action for the valence charm quark,
clover-Wilson fermions for the valence light quarks and HISQ sea quarks. The
spectrum is calculated with a lightest pion mass around 220 MeV and two lattice
spacings ($a\sim0.12$ fm and 0.09 fm) are used to extrapolate to continuum
limit. Our preliminary results are consistent with the currently measured
baryon spectrum, except for the isospin-averaged $J=1/2$ $\Xi_{cc}$ which is
approximately $2 \sigma$ above the SELEX observed value. We predict the
yet-to-be-discovered double and triple-charm baryons $\Xi_{cc}^*$,
$\Omega_{cc}$, $\Omega_{cc}^*$, $\Omega_{ccc}$ to have masses 3665(42)(29) MeV,
3694(40)(45) MeV, 3739(35)(21) MeV and 4782(24)(28) MeV, respectively.
