Crystal symmetry plays a central role in governing a wide range of fundamental physical phenomena. One example is nonlinear optical second harmonic generation (SHG), which requires inversion symmetry breaking. We report a unique stacking-induced SHG in graphene trilayers, whose individual monolayer sheet is centrosymmetric. Depending on layer stacking sequence, we observe a strong optical SHG in a Bernal ABA-stacked non-centrosymmetric trilayer, while it vanishes in a rhombohedral ABC-stacked one, which preserves inversion symmetry. This highly contrasting SHG due to the distinct stacking symmetry enables us to map out the ABA and ABC crystal domains in an otherwise homogeneous graphene trilayer. The extracted second-order nonlinear susceptibility of the ABA trilayer is surprisingly large, comparable to the best known two-dimensional semiconductors enhanced by excitonic resonance. Our results reveal a novel stacking order-induced nonlinear optical effect, as well as unleash the opportunity for studying intriguing physical phenomena predicted for stacking-dependent ABA and ABC graphene trilayers.