We determined the crystal structure of Cs$_2$LiRuCl$_6$, which was synthesized first in this work, and investigated its magnetic properties. Cs$_2$LiRuCl$_6$ has a hexagonal structure composed of linear chains of face-sharing RuCl$_6$ and LiCl$_6$ octahedra. In two-thirds of the structural chains, Ru$^{3+}$ and Li$^+$ sites are almost ordered, while in the other chains their sites are disordered. This situation is analogous to the ground state of the antiferromagnetic Ising model on a triangular lattice. Using electron paramagnetic resonance, we evaluated the $g$ factors of Ru$^{3+}$ with effective spin-1/2 as $g_c,{=},2.72$ and $g_{ab},{=},1.50$ for magnetic fields $H$ parallel and perpendicular to the $c$ axis, respectively. Magnetization curves for $H,{parallel},c$ and $H,{perp},c$ are highly anisotropic. However, these magnetization curves approximately coincide when normalized by the $g$ factors. It was found from the magnetization and specific heat results that Cs$_2$LiRuCl$_6$ can be described as a coupled one-dimensional $S,{=},1/2$ Heisenberg-like antiferromagnet with $J/k_{rm B},{simeq},3.7$ K. Three-dimensional ordering occurs at $T_{rm N},{=},0.48$ K. A magnetic phase diagram for $H,{parallel},c$ is also presented.