Phase-matched harmonic conversion of visible laser light into soft x-rays was demonstrated, The recently developed technique of guided-wave frequency conversion was used to upshift light from 800 nanometers to the range from 17 to 32 nanometers. This process increased the coherent x-ray output by factors of 10(2) to 10(3) compared to the non-phase-matched case. This source uses a small-scale (sub-millijoule) high repetition-rate laser and will enable a wide variety of new experimental investigations in linear and nonlinear x-ray science.