In a large bowl, whisk together 3 Tbsp oil, lemon juice, pepper, and zest.
Toss cut chicken (in medium glass bowl) with marinade and set aside.
In a large skillet over medium-high heat, add remaining 1 tablespoon oil and begin to caramelize onions, stirring 2 minutes.
Turn heat down to low and cook onions to golden brown, about 5-6 minutes.
Turn heat back up to medium high, toss in chicken with marinade and cook chicken until browned on all sides and cooked through.
Two minutes before chicken is finished cooking, add sliced kale, and toss to cook.
Serve immediately