Spread the diced onion at the base of the slow-cooker pot. Place the chicken breast atop the onion in an even layer.
Sprinkle the chicken with the cumin, oregano, and a pinch of salt and pepper. Pour the entire jar of salsa verde over the chicken.
Cook on high for 3 hours, or low for 6 hours, cooking times may vary depending on the slow-cooker. Once cooked, shred the chicken with two forks in the slow-cooker. Stir the shredded chicken into the juices. Season with additional salt and pepper, to taste.
Serve over rice or inside tortillas. Top with sour cream (or Greek yogurt), diced scallions, cilantro, and hot sauce, if desired.