  Inelastic neutron scattering reveals a broad continuum of excitations in
Pr$_2$Zr$_2$O$_7$, the temperature and magnetic field dependence of which
indicate a continuous distribution of quenched transverse fields ($\Delta$)
acting on the non-Kramers Pr$^{3+}$ crystal field ground state doublets.
Spin-ice correlations are apparent within 0.2 meV of the Zeeman energy. A
random phase approximation provides an excellent account of the data with a
transverse field distribution $\rho(\Delta)\propto (\Delta^2+\Gamma^2)^{-1}$
where $ \Gamma=0.27(1)$ meV. Established during high temperature synthesis due
to an underlying structural instability, it appears disorder in
Pr$_2$Zr$_2$O$_7$ actually induces a quantum spin liquid.
