The chaos induced by an intrinsic spontaneous-emission noise in an optically injected semiconductor laser is investigated through a single-mode injection model. A method is developed to quantitatively study the scale-dependent noise effect in general, and the noise-induced chaotic feature in particular. We find that noise at an experimentally measured level can induce chaos in the system. This suggests that noise-induced chaos may indeed exist in real systems. Certain required characteristics for noise to induce chaos are identified: the periodic state itself, when subject to weak noise, should undergo a process that is much more diffusive than the Brownian motion, and the adjacent chaotic states should still behave chaotically on certain finite scales when subject to noise. We believe they are generic features for noise to induce chaos. The correlation dimension of the clean and noisy attractors is also calculated to study noise-induced changes in the geometrical structure of the attractors.