We have synthesized single crystals of CeZnAl$_3$, which is a new member of the family of the Ce-based intermetallics Ce$TX_3$ ($T$ = transition metal, $X$= Si, Ge, Al), crystallizing in the non-centrosymmetric tetragonal BaNiSn$_3$-type structure. Magnetization, specific heat and resistivity measurements all show that CeZnAl$_3$ orders magnetically below around 4.4 K. Furthermore, magnetization measurements exhibit a hysteresis loop at low temperatures and fields, indicating the presence of a ferromagnetic component in the magnetic state. This points to a different nature of the magnetism in CeZnAl$_3$ compared to the other isostructural Ce$T$Al$_3$ compounds. Resistivity measurements under pressures up to 1.8 GPa show a moderate suppression of the ordering temperature with pressure, suggesting that measurements to higher pressures are required to look for quantum critical behavior.
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