A search for a manifestly exotic S=−2 baryon state decaying to Ξ−π−, and its neutral partner decaying to Ξ−π+, has been performed using 220  pb−1 of pp collisions at s√=1.96  TeV collected by the Collider Detector at Fermilab. The Ξ− trajectories were measured in a silicon tracker before their decay, resulting in a sample with low background and excellent position resolution. No evidence was found for S=−2 pentaquark candidates in the invariant mass range of 1600–2100  MeV/c2. Upper limits on the product of pentaquark production cross section times its branching fraction to Ξ−π+,−, relative to the cross section of the well-established Ξ(1530) resonance, are presented for neutral and doubly negative candidates with pT>2  GeV/c and |y|<1 as a function of pentaquark mass. At 1862  MeV/c2, these upper limits for neutral and doubly negative final states were found to be 3.2% and 1.7% at the 90% confidence level, respectively.