The Advanced X-ray Imaging Satellite (AXIS) is a probe-class mission concept with a large collecting area with a point-spread-function of order 1 to 2 arcsec. We describe a possible X-ray grating spectrometer (XGS) that could be added to AXIS with minimal design changes to the telescope itself and costs a small fraction of the total mission budget. The XGS would be based on critical-angle transmission (CAT) gratings, a technology already matured for Arcus and Lynx. Using detailed ray-tracing, we investigate several options for subaperturing that provide a trade-off between effective area and spectral resolving power. Depending on how much of the full aperture is covered with gratings (e.g., 17% to 100%), we find a high spectral resolving power up to λ / Δλ = 4000 can be achieved with effective area of 1500 cm² in the 1.2 to 2.8 nm range or λ / Δλ = 6000 with effective area 500 cm². An important benefit of CAT gratings is that they are mostly transparent at high energies, and thus hard x-rays can still be used for simultaneous imaging spectroscopy. We study different grating sizes and other enhancements, but even in the basic configuration an XGS can be added to AXIS to provide high-resolution spectral capabilities, opening a range of new science investigations. Our ray-tracing shows that this concept is mature and can be added to AXIS with minimal impact on other instruments. We discuss one exemplary science case that would be enabled by the XGS.