This note presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a non negligible time delay. The proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants (chain observer). Conditions are given ensuring global exponential convergence to zero of the observation error for any given the delay in the measurements. The implementation of the observer is simple and computer simulations demonstrate its effectiveness.