To prepare the pickled onions, place onions, lime juice and salt in a bowl and toss well. Let sit for 15 minutes or longer; set aside until you're ready to assemble bowls.
Meanwhile, place the chicken cubes in a medium bowl and season with all of the spices (cumin through cayenne.) Toss well to coat evenly.
Heat olive oil in a large sauté pan over medium-high heat. Add chicken and sauté until cooked through and slightly browned, about 7-9 minutes; set aside until you're ready to assemble bowls.
To assemble bowls, divide cooked quinoa evenly between four dishes. Top with equal parts of the sautéd chicken, avocado slices, pico de gallo and pickled onions. Serve warm, room temperature or chilled.