Preheat oven to 350°F and lightly grease a 9x13-inch baking dish. Set aside.
Coat both sides of the chicken breasts in taco seasoning. If using taco seasoning that does not include salt, generously sprinkle both sides with salt as well.
Heat a large skillet with a lid over medium-high heat. Grease with cooking spray or a drizzle of olive oil. Add chicken breasts to the pan and cook until browned, 2 to 3 minutes. Flip and repeat with the second side. Add enough water to the pan to come up about 1/2-inch.
Bring to a simmer, cover the pan and cook for 6 to 10 minutes (longer with very large chicken breasts), until an instant-read thermometer inserted into the thickest part of the meat reads 165°F. If at any time the water level gets low, add a bit more water to the pan.
Transfer chicken to a cutting board to rest and discard any juices from the pan. Return the pan to the stove and grease with cooking spray or a little olive oil and heat over medium heat. Add onions and 1/4 teaspoon salt and cook 5 to 7 minutes, until onions begin to turn translucent around the edges. If at any time they begin to brown, turn down the heat.
Use two forks to shred the chicken breasts, and combine shredded chicken, onions, and sour cream in a large bowl. Mix well and add salt and pepper to taste. Set aside.