In this paper, we present the design of a non-classical observer that constructs estimates of the state of continuous nonlinear systems at remote locations. The system is connected to the remote location through a communication channel which can only transmit limited amounts of data per unit of time. The observer is designed with the objective that it is as data-efficient as possible whilst possessing a certain robustness towards communication losses without any feedback in the communication channel. We provide bounds for the sufficient data-rate to implement the observer. We apply the theory to the problem of observing the Lorenz system over a channel with minimal data-rates.