Melt butter in a large, heavy-bottomed pot over medium-high heat. Once butter is melted, add the chicken. Cook for 3-5 minutes per side until browned. Remove from pan and set aside.
Add the onions, celery, carrots, garlic, and bell pepper to the pan. Saute for 10 to 15 minutes, or until the vegetables start to brown a bit around the edges.
Add the chicken, broth, salt, and pepper to the pot. Cover and simmer over medium-low heat for 30-40 minutes.
Pull the chicken from the pot and shred with two forks or with the paddle attachment of a stand mixer. Add the chicken back to the pot then stir in the kale. Cook for 2-3 minutes until kale is fully wilted.
Add the lemon juice and then taste soup for seasoning, adding additional salt and pepper if needed. Spoon into individual bowls and serve!