We report the most sensitive direct search for pair production of fourth-generation bottomlike chiral quarks (b′) each decaying promptly to tW. We search for an excess of events with an electron or muon, at least five jets (one identified as due to a b or c quark), and an imbalance of transverse momentum by using data from pp collisions collected by the CDF II detector at Fermilab with an integrated luminosity of 4.8  fb−1. We observe events consistent with background expectation, calculate upper limits on the b′ pair-production cross section (σbb′≲30  fb for mb′>375  GeV/c2), and exclude mb′<372  GeV/c2 at 95% confidence level assuming a 100% branching ratio of b′ to tW.