The PPSZ algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable 3-SAT formulas can be found in expected running time at most \Oc(1.3071^n). Using the technique of limited independence, we can derandomize this algorithm yielding \Oc(1.3071^n) deterministic running time at most.