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 $zsim1-3$ star-forming galaxies recently found based on ionized gas kinematics alone.
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