  We perform ab-initio Quantum Monte Carlo simulations of para-hydrogen
(pH$_2$) at $T=0$ K confined in carbon nanotubes (CNT) of different radii. The
radial density profiles show a strong layering of the pH$_2$ molecules which
grow, with increasing number of molecules, in solid concentric cylindrical
shells and eventually a central column. The central column can be considered an
effective one-dimensional (1D) fluid whose properties are well captured by the
Tomonaga-Luttinger liquid theory. The Luttinger parameter is explicitly
computed and interestingly it shows a non-monotonic behavior with the linear
density similar to what found for pure 1D $^3$He. Remarkably, for the central
column in a (10,10) CNT, we found an ample linear density range in which the
Luttinger liquid is (i) superfluid and (ii) stable against a weak disordered
external potential, as the one expected inside realistic pores. This superfluid
behavior could be experimentally revealed in bundles of carbon nanotubes, where
deviations from classical inertial values associated with superfluid density
could be measured via torsional oscillator techniques. In summary, our results
suggest that pH$_2$ within carbon nanopores could be a practical realization of
the long sought-after, elusive superfluid phase of parahydrogen.
