Heat a skillet over medium-high heat and add the chicken thighs, skin side down. Cook for about 5 minutes until golden brown, then flip and brown the other side for another 5 minutes, releasing a fragrant, smoky aroma.
While the chicken browns, chop the carrots, celery, and onion into bite-sized pieces. Arrange them in the slow cooker as a flavorful vegetable base.
Transfer the browned chicken thighs to the slow cooker on top of the vegetables. Add the minced garlic, bay leaf, and thyme sprig for aromatic depth.
Pour the chicken broth over the ingredients until they are just covered, then set the slow cooker to low and cook for 6 to 8 hours, allowing the flavors to meld and the chicken to become tender.
Once cooking is complete, carefully remove the chicken thighs, shred the meat with two forks, and return it to the slow cooker to reheat in the broth.
Taste the broth and season with salt and pepper as needed. Stir in a splash of lemon juice to brighten the flavors and add a fresh zing.