In this paper, we propose an algorithm for tracking cells that also provides lineage information. Our approach incorporates cell spawning into the random finite set dynamic model of the cell population, which allows the Bayes multi-object filter to capture information on the cells ancestries. A generalized Labeled Multi-Bernoulli (GLMB) filter (with cell spawning model) is applied to track the cells using detections extracted from time lapse video data. Numerical results on a set of stems cells demonstrate the capability of the proposed solution to track the time-varying number of cells as well as their ancestries.