A bitter-tasting compound called saponin coats the outside of quinoa seeds, requiring a quick rinse to remove it. But check the package: some brands come pre-rinsed, saving you a step.
Bring water and quinoa to a boil in a medium saucepan over high heat. Reduce heat to maintain a simmer, cover and cook until just tender, about 15 minutes. Remove from heat and fluff with a fork.
Meanwhile, whisk apricot jam, vinegar and cayenne in a medium bowl. Transfer 3 tablespoons to a small bowl and stir in ginger; set aside. Add almonds, apricots, olives, parsley and 1/4 teaspoon salt to the medium bowl and stir to combine. Stir in the quinoa and cover to keep warm.
Heat oil in a large skillet over medium heat. Add chicken and sprinkle with the remaining 1/4 teaspoon salt. Cook, turning occasionally, until well browned on both sides, 6 to 8 minutes total.
Add the reserved jam mixture and reduce heat to medium-low. Cover and cook until the chicken's internal temperature reaches 165°F and the sauce glazes the chicken, about 3 minutes more. Serve the chicken with the quinoa and drizzled with any drippings from the pan.
