Heat oil in a large, non-stick skillet or wok over medium-high heat. When hot and in batches so as to be careful not to overcrowd the pan, cook the chicken until golden brown on both sides and cooked through, 2-3 minutes per side. Transfer cooked chicken to a plate and continue, adding oil if your skillet seems dry as needed, until all the chicken is browned and cooked through.
In the same skillet (still over medium-high heat), add the broccoli florets and 1/4 cup of water to the skillet. Cook, stirring, until the water has completely evaporated, about 2 minutes.
Add the sauce to the skillet with the broccoli and cook, stirring, until the sauce just begins to thicken, about 2 minutes.
Add the chicken and any of it's juices back into the skillet with the broccoli and sauce. Simmer, stirring, until the sauce is thick and coats the chicken evenly, about 2 to 4 more minutes.
Serve and enjoy!