  We directly measure the low energy excitation modes of the quantum Ising
magnet LiHoF$_4$ using microwave spectroscopy. Instead of a single electronic
mode, we find a set of collective electronuclear modes, in which the spin-$1/2$
Ising electronic spins hybridize with the bath of spin-$7/2$ Ho nuclear spins.
The lowest-lying electronuclear mode softens at the approach to the quantum
critical point, even in the presence of disorder. This softening is rapidly
quenched by a longitudinal magnetic field. Similar electronuclear structures
should exist in other spin-based quantum Ising systems.
