Music source separation performance has greatly improved in recent years with the advent of approaches based on deep learning. Such methods typically require large amounts of labelled training data, which in the case of music consist of mixtures and corresponding instrument stems. However, stems are unavailable for most commercial music, and only limited datasets have so far been released to the public. It can thus be difficult to draw conclusions when comparing various source separation methods, as the difference in performance may stem as much from better data augmentation techniques or training tricks to alleviate the limited availability of training data, as from intrinsically better model architectures and objective functions. In this paper, we present the synthesized Lakh dataset (Slakh) as a new tool for music source separation research. Slakh consists of high-quality renderings of instrumental mixtures and corresponding stems generated from the Lakh MIDI dataset (LMD) using professional-grade sample-based virtual instruments. A first version, Slakh2100, focuses on 2100 songs, resulting in 145 hours of mixtures. While not fully comparable because it is purely instrumental, this dataset contains an order of magnitude more data than MUSDB18, the {\it de facto} standard dataset in the field. We show that Slakh can be used to effectively augment existing datasets for musical instrument separation, while opening the door to a wide array of data-intensive music signal analysis tasks.