  We show that the simplest, and currently favoured, theoretical realizations
of cosmic inflation yield a sharp prediction for the running of the spectral
index $\alpha_\mathrm{S}$. Using latest cosmological data, we compute its
marginalized posterior probability distribution over the space of nearly 300
models of single-field slow-roll inflation. The most probable value is
$\alpha_\mathrm{S}=-6.3 \times 10^{-4}$, lying within the $98\%$ credible
interval $-1.8 \times 10^{-3}< \alpha_\mathrm{S}< -9.1 \times 10^{-5}$. Within
the landscape of all the proposed slow-roll inflationary models, positive
values for the running are therefore disfavoured at more than three-sigma.
