Large data requirements are often the main hurdle in training neural networks. Convolutional neural network (CNN) classifiers in particular require tens of thousands of pre-labeled images per category to approach human-level accuracy, while often failing to generalized to out-of-domain test sets. The acquisition and labelling of such datasets is often an expensive, time consuming and tedious task in practice. Synthetic data provides a cheap and efficient solution to assemble such large datasets. Using domain randomization (DR), we show that a sufficiently well generated synthetic image dataset can be used to train a neural network classifier that rivals state-of-the-art models trained on real datasets, achieving accuracy levels as high as 88% on a baseline cats vs dogs classification task. We show that the most important domain randomization parameter is a large variety of subjects, while secondary parameters such as lighting and textures are found to be less significant to the model accuracy. Our results also provide evidence to suggest that models trained on domain randomized images transfer to new domains better than those trained on real photos. Model performance appears to remain stable as the number of categories increases.