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The next generation of cellular networks will be characterized by softwarized, open, and disaggregated architectures exposing analytics and control knobs to enable network intelligence. How to realize this vision, however, is largely an open problem. In this paper, we take a decisive step forward by presenting and prototyping OrchestRAN, a novel orchestration framework that embraces and builds upon the Open RAN paradigm to provide a practical solution to these challenges. OrchestRAN has been designed to execute in the non-real-time RAN Intelligent Controller (RIC) and allows Network Operators (NOs) to specify high-level control/inference objectives (i.e., adapt scheduling, and forecast capacity in near-real-time for a set of base stations in Downtown New York). OrchestRAN automatically computes the optimal set of data-driven algorithms and their execution location to achieve intents specified by the NOs while meeting the desired timing requirements. We show that the problem of orchestrating intelligence in Open RAN is NP-hard, and design low-complexity solutions to support real-world applications. We prototype OrchestRAN and test it at scale on Colosseum. Our experimental results on a network with 7 base stations and 42 users demonstrate that OrchestRAN is able to instantiate data-driven services on demand with minimal control overhead and latency.