  We report the discovery of bulk superconductivity (SC) at 6.1 K in a
quasi-one-dimensional (Q1D) chromium pnictide K$_2$Cr$_3$As$_3$ which contains
[(Cr$_3$As$_3$)$^{2-}$]$_{\infty}$ double-walled subnano-tubes with
face-sharing Cr$_{6/2}$ (As$_{6/2}$) octahedron linear chains in the inner
(outer) wall. The material has a large electronic specific-heat coefficient of
70$\sim$75 mJ K$^{-2}$ mol$^{-1}$, indicating significantly strong electron
correlations. Signature of non-Fermi liquid behavior is shown by the linear
temperature dependence of resistivity in a broad temperature range from 7 to
300 K. Unconventional SC is preliminarily manifested by the estimated upper
critical field exceeding the Pauli limit by a factor of three to four. The
title compound represents a rare example that possibly unconventional SC
emerges in a Q1D system with strong electron correlations.
