In this paper, control theory is used to formalize finite-time chaos synchronization as a nonlinear finite-time observer design issue. This paper introduces a finite-time observer for nonlinear systems that can be put into a linear canonical form up to an output injection. The finite-time convergence relies on the homogeneity properties of nonlinear systems. The observer is then applied to the problem of secure data transmission based on the finite-time chaos synchronization and the two-channel transmission method.