Green chile grits are a thing in certain parts of the Desert Southwest, notably the stretch between Arizona and El Paso. There’s a reason for this.
Green chiles, usually a variant of the Anaheim chile — Big Jim is the most famous — are wildly popular from Baja, Sonora and Chihuahua to Arizona, New Mexico, southern Colorado and West Texas. As for the grits, once you remember that the Anglo settlement of this region was initially dominated by people from the American South, well, seeing grits on a menu in, say, Bisbee, Arizona, or El Paso makes a lot more sense.