Chaotic Compressive Sensing (ChaCS) is a nonlinear compressive sensing approach using chaos systems. This paper extends the ChaCS to perform the online estimation of sparse time-varying signals. An online estimation structure is proposed and a sparsity-constrained recursive least-squares objective function is formulated. The sparse time-varying signals are estimated through iterative reweighted nonlinear least-square algorithm by minimizing the objective function. The Henon system is taken as examples to expose the estimation performance of frequency sparse time-varying signals. Numerical simulations illustrate the effectiveness of the proposed method.