A recent study reported oscillatory expression of a negatively autoregulated gene incorporated into the E. coli chromosome. Oscillations in the intracellular concentration of the bacteriophage lambda transcriptional repressor Cro had a period of one cell cycle, and phase shifts were observed when the gene circuit was integrated into different chromosomal loci. It is necessary to explain the cause of these oscillations in order for synthetic biologists to predictably design genetic circuits in E. coli. I report computational attempts to test which biomolecular mechanisms might give rise to oscillations and phase shifts. Oscillations are not expected for a simple negative feedback circuit, but might arise when one accounts for cell-cycle phenomena (e.g. chromosome replication, gene doubling, cell division, and cell growth). I simulated stochastic biochemical reactions while accounting for these phenomena and other possible molecular events affecting Cro expression such as transient changes in DNA-binding associated with chromosome conformational changes during replication. Simulations accounted for repressor dimerization and non-specific DNA binding using an equilibrium approximation in order to reduce computation time. To facilitate comparison with experimental data, simulations were carried out for cell lineages of seven generations. The maturation and photobleaching of a fluorescent protein reporter was also simulated to match experimental output. Simulated data was compared to experimental data by examining the average Cro expression level as a function of the fraction of cell cycle elapsed and the autocorrelation of Cro-expression time traces.