Season the chicken thighs with a little salt and pepper, then heat olive oil in your heavy-bottomed pot over medium-high heat. Sear the chicken until golden brown on both sides, about 5 minutes per side, then remove and set aside.
In the same pot, add chopped onions, sliced carrots, and chopped celery. Sauté until fragrant and vegetables are slightly softened, about 7 minutes, stirring occasionally.
Return the chicken to the pot, then pour in the chicken broth. Add thyme and bring the mixture to a gentle simmer. Cover and cook on low heat for about 30 minutes, until the chicken is tender and flavorful.
Remove the chicken from the pot and set aside to cool slightly. Meanwhile, add rinsed rice to the broth and vegetables, stirring well. Continue simmering uncovered for about 15 minutes, until the rice is fluffy and tender.
While the rice cooks, shred the chicken into bite-sized pieces, discarding the bones if any. Return the shredded chicken to the pot, stirring to combine.
Taste the soup and adjust seasoning with salt and pepper as needed. Squeeze a splash of lemon juice into the pot to brighten the flavors, then stir in chopped parsley.
Serve the soup hot, garnished with extra parsley if desired, and enjoy the comforting, flavorful broth with tender chicken and fluffy rice.
