The first detailed measurements of the centrality dependence of strangeness production in p-A collisions are presented. Lambda and Kshort dn/dy distributions from 17.5 GeV/c p-Au collisions are shown as a function of grey track multiplicity and the estimated number of collisions, nu, made by the proton. The nu dependence of the Lambda yield deviates from a scaling of p-p data by the number of participants, increasing faster than this scaling for nu<=5 and saturating for larger nu. A slower growth in Kshort multiplicity with nu is observed, consistent with a weaker nu dependence of K-Kbar production than Y-K production.