• Pat the chicken dry with a paper towel; season generously with salt and pepper.

In a large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the chicken, skin side down, and cook until the skin is well browned, 5 to 6 minutes. Turn and cook until the meat is firm and cooked through, 3 to 5 minutes. Transfer to a plate. Do not clean the pan.
While the chicken cooks, prepare the remaining ingredients.

• Peel and thinly slice enough shallots to measure ⅓ cup [⅔ cup].
• Thinly slice the olives crosswise, checking for any pits.
• Rinse the capers.
• Zest and juice the lemon, keeping the zest and juice separate.
• Strip the parsley leaves from the stems; coarsely chop the leaves for garnish.

In the same pan used for the chicken, if dry, add 1 to 2 teaspoons oil. Warm over medium-high heat until hot but not smoking. Add the shallots, olives, and capers and cook, stirring occasionally, until the shallots are softened, 2 to 3 minutes. Stir in the lemon zest, 2 tablespoons [¼ cup] lemon juice, ¼ cup [½ cup] water, and 1 tablespoon [2 TBL] butter (from your pantry) or 1 to 2 teaspoons oil.
Working in batches if needed, add the kale and spinach and cook, stirring occasionally, until the greens are wilted and the sauce has thickened to a glaze, 2 to 3 minutes. Remove from the heat and season to taste with salt and pepper.

Transfer the greens to individual plates and top with the chicken. Garnish with the parsley and serve.