  We examine the low frequency spin susceptibility of the paramagnetic phase of
the quantum Ising chain in transverse field at temperatures well below the
energy gap. We find that the imaginary part is dominated by rare quantum
processes in which the number of quasiparticles changes by an odd number. We
obtain exact results for the NMR relaxation rate in the low temperature limit
for the integrable model with nearest-neighbor Ising interactions, and derive
exact universal scaling results applicable to generic Ising chains near the
quantum critical point. These results resolve certain discrepancies between the
energy scales measured with different experimental probes in the quantum
disordered paramagnetic phase of the Ising chain system CoNb$_{2}$O$_{6}$.
