Contextuality is one of the most fundamental properties of quantum mechanics, distinguishing it from classical physics without a need for nonlocality or entanglement. It is also a critical resource for exponential speedup in universal surface-code quantum computing. Our result is the first experiment violating a noncontextuality inequality with an indivisible system where entanglement cannot be defined which also addresses all known major loopholes, such as the detection, compatibility and individual-existence loopholes. Violating noncontextuality with superconducting circuits, a leading candidate for implementing surface-code quantum computing, comprises an important conceptual milestone in demonstrating their suitability for quantum technological applications.