Stir the chili powder and cumin in a medium bowl. Add the chicken and toss to coat.
Heat the oil in a heavy 12-inch skillet over high heat. Add the chicken and cook until it's blackened and cooked through, stirring often. Remove the chicken from the skillet.
Stir the salsa and water in the skillet and cook until the mixture is hot and bubbling. Divide the greens among 6 plates. Top with the chicken and salsa mixture.