  Quantum gases of doubly-polar molecules represent appealing frameworks for a
variety of cross-disciplinary applications, encompassing quantum simulation and
computation, controlled quantum chemistry and precision measurements. Through a
joint experimental and theoretical study, here we explore a novel class of
ultracold paramagnetic polar molecules combining lithium alkali and chromium
transition metal elements. Focusing on the specific bosonic isotopologue
$^{6}$Li$^{53}$Cr, leveraging on the Fermi statistics of the parent atomic
mixture and on suitable Feshbach resonances recently discovered, we produce up
to $50\times10^3$ ultracold LiCr molecules at peak phase-space densities
exceeding 0.1, prepared within the least-bound rotationless level of the LiCr
electronic $sextet$ ground state $X^6\Sigma^+$. We thoroughly characterize the
molecular gas, demonstrating the paramagnetic nature of LiCr dimers and the
precise control of their quantum state. We investigate their stability against
inelastic processes and identify a parameter region where pure LiCr samples
exhibit lifetimes exceeding 0.2 s. Parallel to this, we employ state-of-the-art
quantum-chemical calculations to predict the properties of LiCr ground and
excited electronic states. We identify efficient paths to coherently transfer
weakly-bound LiCr dimers to their absolute ground state, to deliver ultracold
gases of doubly-polar molecules with significant electric (3.3 D) and magnetic
($5\,\mu_\text{B}$) dipole moments.
