A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability from cell to cell. Here we focus on the case where single-cell fluorescent protein imaging time series data are available for a population of cells. Based on van Kampen's linear noise approximation, we derive a dynamic state space model for molecular populations which is then extended to a hierarchical model. This model has potential to address the sources of variability relevant to single-cell data, namely, intrinsic noise due to the stochastic nature of the birth and death processes involved in reactions and extrinsic noise arising from the cell-to-cell variation of kinetic parameters. In order to infer such a model from experimental data, one must also quantify the measurement process where one has to allow for nonmeasurable molecular species as well as measurement noise of unknown level and variance. The availability of multiple single-cell time series data here provides a unique testbed to fit such a model and quantify these different sources of variation from experimental data. ; Comment: Published in at http://dx.doi.org/10.1214/13-AOAS669 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)