1. Preheat slow cooker to high. Add the chicken broth.
2. Cut chicken into 1 inch pieces. Peel and slice carrots into rounds. Chop celery. Peel and dice onion. Dice leek. Juice and zest lemon. Chop tarragon.
3. In a large pan, heat ½ of the oil over medium high heat. place chicken in the pan, season with ½ of the salt and pepper.
4. Cook until golden, about 3-4 minutes per side; transfer the chicken to the slow cooker. Turn slow cooker to low.
5. Add the remaining olive oil and onion to the pan and cook over medium heat until the onions begin to soften.
6. Add the celery, leek, and garlic and cook for about 2 minutes; season with remaining salt and pepper.
7. Slowly add a ladle full of warmed chicken broth, scraping the browned bits from the bottom of the pan.
8. Transfer veggies to the slow cooker. Add rice and carrots to slow cooker, cover and cook on low for 3 hours, or until rice is tender.
9. Make sure chicken is cooked through until an internal temperature of 165F is reached as well.
10. Stir in lemon juice and zest, and season with salt and pepper, to taste. Sprinkle with tarragon immediately before serving.