We have made the first complete measurements of the London penetration depth $lambda(T)$ of CeCoIn5, a quantum-critical metal where superconductivity arises from a non-Fermi-liquid normal state. Using a novel tunnel diode oscillator designed to avoid spurious contributions to $lambda(T)$, we have established the existence of intrinsic and anomalous power-law behaviour at low temperature. A systematic analysis raises the possibility that the unusual observations are due to an extension of quantum criticality into the superconducting state.
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