Season the chicken breasts with a pinch of salt and pepper. Heat a skillet over medium-high heat, add olive oil, and sear each side for about 2-3 minutes until golden brown. Transfer the seared chicken to a plate; this step adds flavor and color, but can be skipped if pressed for time.
In the slow cooker, combine the minced garlic, lemon juice, chicken broth, and rinsed capers. Stir well to blend the flavors. Nestle the seared chicken breasts into the sauce, ensuring they are mostly submerged.
Cover and cook on low for 4 hours or on high for about 2-3 hours until the chicken is tender and cooked through. The house will fill with a fragrant lemon aroma, signaling the flavors are melding.
About 30 minutes before serving, melt the butter in a small saucepan over medium heat. Pour the melted butter into the slow cooker and gently stir to incorporate, enriching the sauce with a silky sheen and depth of flavor.
Once the chicken is tender and the sauce has thickened slightly, carefully remove the chicken breasts with tongs and place on serving plates. Spoon the bright, caper-studded sauce over the top.
Garnish with additional fresh herbs if desired, and serve immediately alongside pasta, rice, or crusty bread to soak up that flavorful, lemony sauce. Enjoy this bright, comforting dish with minimal fuss!
