In this paper, a novel First-Order Sliding Mode (FOSM) Observer to estimate the state of a Linear Time-Invariant (LTI) system is presented. The main difference with other FOSM schemes is the selection of a time-varying surface, which is constructed using the dynamical structure of the system. The choice of this surface leads to finite-time convergence of the estimation error for any observable LTI system. The main advantage of this approach is the easiness in the design of the estimator gains, which is done in a linear framework.