Season chicken breasts with salt and pepper and dredge lightly in flour. Heat olive oil in a skillet over medium-high heat and brown each breast 1–2 minutes per side for color (optional).
Place chicken in a single layer in the slow cooker. Whisk together chicken broth, lemon juice, garlic, and lemon zest; pour over the chicken. Scatter capers and dot with butter.
Cover and cook on LOW for 3–4 hours or on HIGH for 1.5–2 hours, until the chicken reaches 165°F and is tender. Begin checking near the lower end of the time range.
Remove chicken and keep warm. Simmer the liquid in a saucepan until reduced and glossy (5–8 minutes), then whisk in a tablespoon of butter. Or, for a shortcut, stir in a cornstarch slurry (1 tbsp cornstarch + 1 tbsp water) and cook on HIGH in the crockpot for 10–15 minutes.
Plate chicken over pasta, rice, or potatoes, spoon sauce over the top, and garnish with chopped parsley and extra lemon zest if desired.
Notes
To make gluten-free, skip the flour and thicken the sauce with a cornstarch slurry.
Store leftovers in an airtight container in the fridge for 3–4 days.
For a creamier sauce, stir in 2–3 tablespoons heavy cream after reducing.