We numerically report on an optical chaos signal generation scheme based on a semiconductor laser subject to intensity-modulated (IM) optical injection. In this scheme, the characteristics of the chaos signal obtained by destabilizing period-one nonlinear dynamics are numerically investigated. With the aid of bifurcation diagrams and the 0-1 tests for chaos, the chaotic dynamics excited by continuous-wave and IM optical injection are located, and the effects of injection and modulation parameters on chaotic regions are illustrated. Moreover, effective bandwidths and auto-correlation characteristics of chaos signals from the IM optical injection system are systematically investigated. The results show that although chaotic signals under the IM optical injection scenario have a limitation in unambiguous range detection in most parameter regions, wideband chaotic dynamics in large injection and modulation parameter regions can be easily achieved. This study paves the way for potential applications requiring no time-delay signature and broad bandwidth chaos, such as high-speed chaos communications and random bit generation.