  We have measured the heat capacities of $\delta-$Pu$_{0.95}$Al$_{0.05}$ and
$\alpha-$Pu over the temperature range 2-303 K. The availability of data below
10 K plus an estimate of the phonon contribution to the heat capacity based on
recent neutron-scattering experiments on the same sample enable us to make a
reliable deduction of the electronic contribution to the heat capacity of
$\delta-$Pu$_{0.95}$Al$_{0.05}$; we find $\gamma = 64 \pm 3$
mJK$^{-2}$mol$^{-1}$ as $T \to 0$. This is a factor $\sim 4$ larger than that
of any element, and large enough for $\delta-$Pu$_{0.95}$Al$_{0.05}$ to be
classed as a heavy-fermion system. By contrast, $\gamma = 17 \pm 1$
mJK$^{-2}$mol$^{-1}$ in $\alpha-$Pu. Two distinct anomalies are seen in the
electronic contribution to the heat capacity of
$\delta-$Pu$_{0.95}$Al$_{0.05}$, one or both of which may be associated with
the formation of the $\alpha'-$ martensitic phase. We suggest that the large
$\gamma$-value of $\delta-$Pu$_{0.95}$Al$_{0.05}$ may be caused by proximity to
a quantum-critical point.
