Heat the oil in a large, deep nonstick skillet set over medium-high heat. Add the chicken in a single layer, working in batches as needed, and cook, undisturbed, until a golden-brown crust forms, about 3 minutes. Flip the chicken and continue to cook until both sides are golden brown, 2 to 3 minutes. Transfer the cooked chicken to a plate and set aside.
Reduce the heat to medium and add the broccoli to the pan along with 1/4 cup of water. Cook, scraping up any browned bits, until broccoli is bright green and the water has evaporated, about 3 minutes.
Add the chicken back to the skillet and pour in the sauce. Cook, simmering and stirring occasionally, until the sauce thickens and coats the chicken, about 3 minutes.
Remove from heat and let cool slightly. Serve as is or over prepared rice, if desired.