The first detailed measurements of the centrality dependence of strangeness production in p-A collisions are presented. Lambda and K(S) 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 K(S) multiplicity with nu is observed, consistent with a weaker nu dependence of K&Kmacr; production than YK production.