Quantitative Transmission Ultrasound (QT) is a powerful and emerging imaging paradigm which has the potential to perform true three-dimensional image reconstruction of biological tissue. Breast imaging is an important application of QT and allows non-invasive, non-ionizing imaging of whole breasts in vivo. Here, we report the first demonstration of breast tissue image classification in QT imaging. We systematically assess the ability of the QT images' features to differentiate between normal breast tissue types. The three QT features were used in Support Vector Machines (SVM) classifiers, and classification of breast tissue as either skin, fat, glands, ducts or connective tissue was demonstrated with an overall accuracy of greater than 90%. Finally, the classifier was validated on whole breast image volumes to provide a color-coded breast tissue volume. This study serves as a first step towards a computer-aided detection/diagnosis platform for QT.