This paper proposes a new class of observers, called adaptive impulsive observer (AIO). AIO is capable to give continuous estimation for the states of a continuous nonlinear system by using the output of the system just at discrete impulse times. This is very significant in applications when establishing a continuous link (couple) between system (drive) and observer (response) is impossible. Also, the AIO estimates both states and unknown parameters of the uncertain system while its computational expense is relatively small in comparison with most conventional observers. Through a new theorem asymptotic convergence of the state estimation error is proved and an upper bound on the maximum possible impulse interval is given. The AIO design routine is simplified by modifying conditions of the proposed theorem to a set of linear matrix inequalities (LMIs). Because of these advantages, the AIO is used through a chaotic systems observer-based synchronization scheme. Simulation results confirm the proficiency of the AIO even when the coupling signal is scalar.