The use of needles to access sites within organs is fundamental to many interventional medical procedures both for diagnosis and treatment. Safely and accurately navigating a needle through living tissue to a target is currently often challenging or infeasible because of the presence of anatomical obstacles, high levels of uncertainty, and natural tissue motion. Medical robots capable of automating needle-based procedures have the potential to overcome these challenges and enable enhanced patient care and safety. However, autonomous navigation of a needle around obstacles to a predefined target in vivo has not been shown. Here, we introduce a medical robot that autonomously navigates a needle through living tissue around anatomical obstacles to a target in vivo. Our system leverages a laser-patterned highly flexible steerable needle capable of maneuvering along curvilinear trajectories. The autonomous robot accounts for anatomical obstacles, uncertainty in tissue/needle interaction, and respiratory motion using replanning, control, and safe insertion time windows. We applied the system to lung biopsy, which is critical for diagnosing lung cancer, the leading cause of cancer-related deaths in the United States. We demonstrated successful performance of our system in multiple in vivo porcine studies achieving targeting errors less than the radius of clinically relevant lung nodules. We also demonstrated that our approach offers greater accuracy compared with a standard manual bronchoscopy technique. Our results show the feasibility and advantage of deploying autonomous steerable needle robots in living tissue and how these systems can extend the current capabilities of physicians to further improve patient care.