  Strongly diluted Ce$_x$La$_{1-x}$Al$_3$ alloys have been studied by the low
temperature specific heat in order to elucidate the mechanism that determine
their ground state. All alloys with Ce concentrations of $0.0005 \leq x \leq
0.1$ show a $S=1/2$ Kondo behavior. However, the single-ion scaling is observed
only below $x=0.01$. The true single-ion Kondo temperature is small, 0.2 K, and
is identical to that for dilute CeAl$_2$. It is about 20 times smaller than
that for CeAl$_3$, indicating that intersite interactions facilitate
Kondo-screening in CeAl$_3$ and concentrated Ce$_x$La$_{1-x}$Al$_3$ alloys.
