Tomogrophic ultrasound imaging is gaining popularity in breast cancer detection. Reconstructing the acoustic properties of a breast from the ultrasound measurements is stated as a nonlinear inverse problem, which is usually solved by linearized methods because of computational efficiency. However, linearization of the problem reduces the quality of the reconstruction. To improve the accuracy, we developed and tested a three-dimensional nonlinear inversion method that allow for three-dimensional reconstruction of the breast in terms of speed of sound. The method, referred to as contrast source inversion (CSI), uses an integral equation formulation to describe the inverse acoustic scattering problem. The resulting integral equation is solved to reconstruct the unknown contrast (speed-of-sound profile of the breast). The contrast and contrast sources (the product of the contrast with the total field) are iteratively updated by minimizing a cost functional using conjugate gradient directions. In this study, we tested the CSI method on synthetic data retrieved form full-wave simulations for a realistic three-dimensional cancerous breast model. Results show that the CSI method outer performs other conventional methods as it yields speed-of-sound reconstructions that are akin to the model. This shows that the approach offers a contribution to the detection of breast cancer.