  While the vast majority of known physical realizations of the
Tomonaga-Luttinger liquid (TLL) have repulsive interactions defined with the
dimensionless interaction parameter $K_{\rm c}<1$, we here report that
Rb$_2$Mo$_3$As$_3$ is in the opposite TLL regime of attractive interactions.
This is concluded from a TLL-characteristic power-law temperature dependence of
the $^{87}$Rb spin-lattice relaxation rates over broad temperature range
yielding the TLL interaction parameter for charge collective modes $K_{\rm
c}=1.4$. The TLL of the one-dimensional band can be traced almost down to
$T_{\rm c} = 10.4 $~K, where the bulk superconducting state is stabilized by
the presence of a three-dimensional band and characterized by the $^{87}$Rb
temperature independent Knight shift and the absence of Hebel-Slichter
coherence peak in the relaxation rates. The small superconducting gap measured
in high magnetic fields reflects either the importance of the vortex core
relaxation or the uniqueness of the superconducting state stemming from the
attractive interactions defining the precursor TLL.
