The newly discovered CaFe$_4$As$_3$ system displays low-temperature Fermi liquid behavior, with enhanced electron-electron correlations. At high temperatures, the magnetic susceptibility shows Curie-Weiss behavior, with a large temperature-independent contribution. Antiferromagnetic ordering is observed below T$_N$ = (88.0 $pm$ 1.0) K, possibly via a spin density wave (SDW) transition. A remarkably sharp drop in resistivity occurs below T$_2$ = (26.4 $pm$ 1.0) K, correlated with a similarly abrupt increase in the susceptibility, but no visible feature in the specific heat. The electronic specific heat coefficient $gamma$ at low temperatures is close to 0.02 J mol$^{-1}_{Fe}$ K$^{-2}$, but a higher value for $gamma$ ($sim$0.08 J mol$^{-1}_{Fe}$ K$^{-2}$ can be inferred from a linear C$ / $T textit{vs.} T$^2$ just above T$_2$. The Kadowaki-Woods ratio A$/gamma^2$ = 55$*10^{-5}$ $mu Omega$cm mol$^2$ K$^2 $mJ$^{-2}$ is nearly two orders of magnitude larger than that of heavy fermions.
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