This paper describes AbletonOSC, an Open Sound Control API whose objective is to expose the complete Ableton Live Object Model via OSC. Embedded within Live by harnessing its internal Python scripting interface, AbletonOSC allows external processes to exert real-time control over any element of a Live set, ranging from generating new melodic sequences to modulating deeply-nested synthesis parameters. We describe the motivations and historical precedents behind AbletonOSC, provide an overview of its OSC namespace and the classes of functionality that are exposed by the API, and look at a series of applied case studies that demonstrate the new types of musical interface that AbletonOSC enables.