The authors present preliminary measurements of the B meson decays B(sup+)(yields)(eta)(pi)(sup+), B(sup+)(yields)(eta)K(sup+), and B(sup 0)(yields)(eta)K(sup 0). The data were recorded with the BABAR detector at PEP II and correspond to 88.9 x 10(sup 6) B(bar B) pairs produced in e(sup+)e(sup -) annihilation through the(Upsilon)(4S) resonance. They find the branching fractions(Beta)(B(sup+ )(yields)(eta)(pi)(sup+))= (4.2(sub -0.9)(sup+1.0)(+-) 0.3) x 10(sup -6) and(Beta)(B(sup+ )(yields)(eta)K(sup+))= (2.8(sub -0.7)(sup+0.8)(+-) 0.2)x 10(sup -6). They set a 90% CL upper limit of(Beta)(B(sup 0)(yields)(eta)K(sup 0)) < 4.6 x 10(sup -6). The time-integrated charge asymmetries are(Alpha)(sub ch)(B(sup+)(yields) (eta)(pi)(sup+))= -0.51(sub -0.18)(sup+0.20)(+-) 0.01 and(Alpha)(sub ch)(B(sup+)(yields)(eta)K(sup+))= -0.32(sub -0.18)(sup+0.22)(+-) 0.01.