We propose a sequential and adaptive hypothesis test that operates in a completely distributed setting, relying on a sensor network where no single data-fusion center is present. The test is inspired by Chernoff's optimal solution, originally derived in a centralized setting. We compare the performance of our test with the optimal sequential test in sensor networks and provide sufficient conditions for which the proposed test achieves asymptotic optimality, minimizing the expected cost required to reach a decision plus the expected cost of making a wrong decision, when the observation cost per unit time tends to zero. Under these conditions, the proposed test is also shown to be asymptotically optimal with respect to the higher moments of the time required to reach a decision.