  We present deep observations of a $z=1.4$ massive, star-forming galaxy in
molecular and ionized gas at comparable spatial resolution (CO 3-2, NOEMA;
H$\alpha$, LBT). The kinematic tracers agree well, indicating that both gas
phases are subject to the same gravitational potential and physical processes
affecting the gas dynamics. We combine the one-dimensional velocity and
velocity dispersion profiles in CO and H$\alpha$ to forward-model the galaxy in
a Bayesian framework, combining a thick exponential disk, a bulge, and a dark
matter halo. We determine the dynamical support due to baryons and dark matter,
and find a dark matter fraction within one effective radius of $f_{\rm
DM}(\leq$$R_{e})=0.18^{+0.06}_{-0.04}$. Our result strengthens the evidence for
strong baryon-dominance on galactic scales of massive $z\sim1-3$ star-forming
galaxies recently found based on ionized gas kinematics alone.
