Lay the chicken in a single layer in a wide skillet or pot. Season with cumin, garlic powder and oregano.
Pour the salsa and broth over, cover, and bring to a bare simmer. Lower the heat until the surface barely moves; a hard boil makes stringy chicken.
Cook covered 18 to 22 minutes, until the thickest piece reads 160F on an instant-read thermometer. Do not push past it; carryover finishes the job.
Turn off the heat. Shred the chicken directly in the pan with two forks, in the liquid, never on a cutting board.
Let the shredded meat sit in the sauce 5 to 10 minutes off the heat so it drinks the liquid back.
Finish with lime juice, taste for salt, and serve, or cool in the liquid for the week's dinners.