  We have grown the single crystals of CeMg$_3$ and its non-magnetic analogue
LaMg$_3$, which crystallize in the cubic crystal structure with the space group
\textit{Fm\rm{\={3}}m}, and studied their magnetic properties on well oriented
single crystals by measuring the magnetic susceptibility, magnetization and
heat capacity. CeMg$_3$ orders antiferromagnetically with a N\'{e}el
temperature $T_{\rm N}$ of 2.6 K. The specific heat capacity at low temperature
exhibits an enhanced Sommerfeld coefficient of 370 mJ/K$^2$$...$ mol indicating
the heavy fermion nature of CeMg$_3$. An estimation of Kondo temperature
$T_{\rm K}$ was made and found that it is of similar magnitude as that of
$T_{\rm N}$. The reduced value of the magnetization below the ordering
temperature, together with the reduced entropy at the magnetic ordering
temperature and the enhanced low temperature heat capacity indicates that Kondo
effect plays a significant role in this compound. We have performed the
crystalline electric field (CEF) analysis on the magnetic susceptibility and
the heat capacity data and found that the ground state is a $\Gamma_7$ doublet
with an overall splitting of 191 K.
