  We compute the spectral form factor of two integrable quantum-critical many
body systems in one spatial dimension. The spectral form factor of the quantum
Ising chain is periodic in time in the scaling limit described by a conformal
field theory; we also compute corrections from lattice effects and deviation
from criticality. Criticality in the random Ising chain is described by rare
regions associated with a strong randomness fixed point, and these control the
long time limit of the spectral form factor.
