We have studied two-body charmless hadronic decays of B mesons into th
e final states pi pi, K pi and KK. Using 3.3 x 10(6) B (B) over bar pa
irs collected with the CLEO-II detector, we have made the first observ
ation of the decay B-0 --> K(+)pi(-), the sum of B+ --> pi(+)pi(0) and
B+ --> K(+)pi(0) decays, and see strong evidence for the decay B+ -->
K-0 pi(+) (an average over charge-conjugate states is always implied)
. We place upper limits on branching fractions for the remaining decay
modes.