Massive multiple-input multiple-output (MIMO) systems are cellu-lar networks where the base stations (BSs) are equipped with un-conventionally many antennas. Such large antenna arrays offer huge spatial degrees-of-freedom for transmission optimization; in partic-ular, great signal gains, resilience to imperfect channel knowledge, and small inter-user interference are all achievable without exten-sive inter-cell coordination. The key to cost-efficient deployment of large arrays is the use of hardware-constrained base stations with low-cost antenna elements, as compared to today's expensive and power-hungry BSs. Low-cost transceivers are prone to hardware im-perfections, but it has been conjectured that the excessive degrees-of-freedom of massive MIMO would bring robustness to such im-perfections. We herein prove this claim for an uplink channel with multiplicative phase-drift, additive distortion noise, and noise ampli-fication. Specifically, we derive a closed-form scaling law that shows how fast the imperfections increase with the number of antennas.