The axial charge of the nucleon, g_A, is a fundamental quantity in nuclear physics which governs both nuclear beta decay and the nuclear force, and is extremely well-measured experimentally. However, its calculation directly from the underlying theory of QCD has proven frustratingly difficult, calling into question the potential accuracy of lattice QCD applications to nuclear physics. Here, I present the first lattice QCD calculation of g_A to a precision of 1% with control over all systematics, highlighting new computational strategies which have made this calculation possible without the need for next-generation computing power. I also show that already at this level of precision our calculation can provide important constraints on beyond the Standard Model physics.