  Recently co-existence of the ferromagnetism and superconductivity was
reported in the high-pressure region (1.0-1.6 GPa) in UGe$_2$. We performed the
heat capacity measurement on UGe$_2$ under high pressure. At 1.13 GPa, we found
a peak corresponding to the superconducting transition. The superconducting
temperature $T_{SC}$ and ${\it\Delta} C/(\gamma T_{SC})$ are 0.6 K and 0.25,
respectively. The superconducting transition was also confirmed by the
appearance of the Meissner effect in the {\it ac} susceptibility. From these
results, we confirm a bulk nature of the superconductivity in UGe$_2$. The
value of $C/T$ ($\sim$ 95 mJ/moleK$^2$) just above $T_{SC}$ at 1.15 GPa is as
much as 3 times larger than that at ambient pressure, which indicates a large
mass enhancement of quasiparticles under high pressure.
