Circularly-polarized extreme ultraviolet and X-ray radiation is useful for analysing the structural, electronic and magnetic properties of materials. To date, such radiation has only been available at large-scale X-ray facilities such as synchrotrons. Here, we demonstrate the first bright, phase-matched, extreme ultraviolet circularly-polarized high harmonics source. The harmonics are emitted when bi-chromatic counter-rotating circularly-polarized laser pulses field-ionize a gas in a hollow-core waveguide. We use this new light source for magnetic circular dichroism measurements at the M-shell absorption edges of Co. We show that phase-matching of circularly-polarized harmonics is unique and robust, producing a photon flux comparable to linearly polarized high harmonic sources. This work represents a critical advance towards the development of table-top systems for element-specific imaging and spectroscopy of multiple elements simultaneously in magnetic and other chiral media with very high spatial and temporal resolution.