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We report the finding of a novel pairing state in a newly discoveredsuperconductor Na$_2$Cr$_3$As$_3$. This material has a noncentrosymmetricquasi-one-dimensional crystal structure and is superconducting at$T_{\mathrm{C}}\sim$ 8.0 K. We find that the magnetic penetration depth datasuggests the presence of a nodal line $p_z$-wave pairing state with zeromagnetic moment using transverse-field muon-spin rotation (TF-$\mu$SR)measurements. The nodal gap observed in Na$_2$Cr$_3$As$_3$ compound isconsistent with that observed in isostructural (K,Cs)$_2$Cr$_3$As$_3$ compoundsusing TF-$\mu$SR measurements. The observed pairing state is consistent with athree-band model spin-fluctuation calculation, which reveals the $S_z=0$spin-triplet pairing state with the $\sin k_z$ pairing symmetry. Thelong-sought search for chiral superconductivity with topological applicationscould be aided by such a novel triplet $S_z=0$ $p$-wave pairing state.

$\mu$SR study of unconventional pairing symmetry in the quasi-1D Na$_2$Cr$_3$As$_3$ superconductor