We demonstrate the first generation and phase matching of circularlypolarized high harmonics, which are bright enough for X-ray magnetic circular dichroism measurements at the M absorption edges of the magnetic materials Fe, Co and Ni. Circularly polarized light in the extreme ultraviolet (EUV) and soft X-ray regions of the electromagnetic spectrum is extremely useful for exploring chirality-sensitive light-matter interactions. X-ray magnetic circular dichroism (XMCD) makes it possible to extract detailed information about the magnetic state of matter and its interaction with phononic and electronic degrees of freedom on femtosecond time scales and nanometer length scales. Specifically, XMCD can be used to distinguish between spin and orbital contributions to the atomic magnetic moment in ferromagnetic materials, with element-specificity, which is not possible using ultrafast visible laser spectroscopy. To date, circularly polarized EUV and soft X-ray beams were restricted to large-scale electron storage facilities, such as synchrotrons and Xray free electron lasers. Such facilities have great advantages of high peak and average powers in the X-ray region. However, drawbacks include experimental complexity, limited access and temporal resolution, as well as pump/probe jitter.