In this paper, a modulated optical injection system is proposed. It mainly consists of a semiconductor laser subject to a modulated optical injection. It is known that optical injection will force a laser intensity into high-speed periodic oscillation without modulation, while the oscillation will be locked with weak external modulation. However, the route to chaos in such a system is observed and reported for the first time. It is shown that the generated oscillation frequency shifts away from the external frequency when the modulation amplitude becomes sufficiently large. Due to the nonlinearities of the laser, the frequencies are mixed inside the laser cavity, which causes the dynamics to follow a quasi-periodic route to chaos. In addition, the resultant chaotic signal possesses a larger bandwidth than that attainable with constant optical injection alone. Since the system is capable of generating both narrowband photonic microwave signals with low phase variances and chaotic signals with large bandwidths, it is practically important for Doppler and chaotic lidar applications.