How long does cosmic inflation last? We study the transition from a Planck scale quantum-gravity phase to an inflationary phase in the primordial universe, and identify a "cosmic veiling" principle for the transition. Namely, as inflation pushes the Planck scale farther into the past, acting as a cosmic censor, we select a threshold condition for gentle veiling, instead of full censorship. This condition necessitates a smooth transition into a post-Planckian, but pre-inflationary epoch, in which the framework of perturbative field theory is valid. Remarkably, within R+R2 inflation, we find that the cosmic veiling principle fixes the duration of inflation in terms of the coupling constants of the theory. We determine the effects on the primordial power spectrum of cosmological perturbations and discuss the possibility for future observations.