  We report the synthesis of powder and single-crystal samples of the cerium
pyrohafnate and their characterization using neutron diffraction,
thermogravimetry and X-ray absorption spectroscopy. We evaluate the amount of
non-magnetic Ce$^{4+}$ defects and use this result to interpret the spectrum of
crystal-electric field transitions observed using inelastic neutron scattering.
The analysis of these single-ion transitions indicates the dipole-octupole
nature of the ground state doublet and a significant degree of spin-lattice
coupling. The single-ion properties calculated from the crystal-electric field
parameters obtained spectroscopically are in good agreement with bulk magnetic
susceptibility data down to about 1 K. Below this temperature, the behavior of
the magnetic susceptibility indicates a correlated regime without showing any
sign of magnetic long-range order or freezing down to 0.08 K. We conclude that
Ce$_2$Hf$_2$O$_{7}$ is another candidate to investigate exotic correlated
states of quantum matter such as the octupolar quantum spin ice recently argued
to exist in the isostructural compounds Ce$_2$Sn$_2$O$_7$ and
Ce$_2$Zr$_2$O$_7$.
