Heat a large soup pot over medium heat and add a tablespoon of olive oil. Once shimmering, add the chopped onion and cook until translucent and fragrant, about 3-4 minutes.
Add the minced garlic and diced carrots to the pot. Sauté for another 2 minutes, filling the kitchen with a warm, garlicky aroma.
Push the vegetables slightly to one side and place the chicken thighs in the pot. Sear them for about 5 minutes on each side until they develop a light golden crust.
Pour in the chicken broth, making sure to scrape up any flavorful bits stuck to the bottom of the pot. Bring to a gentle simmer and reduce heat to low.
Add the diced celery and dried thyme. Cover the pot and let the chicken simmer for 30-35 minutes, until the meat is tender and falling apart.
Remove the chicken thighs from the pot, and once cooled slightly, shred the meat into bite-sized pieces. Return the shredded chicken to the soup.
Add the uncooked rice to the simmering broth. Stir well, cover, and cook for about 15 minutes until the rice is tender and the soup has thickened slightly.
Season the soup with salt and pepper to taste, adjusting the seasoning as needed. Let it simmer uncovered for another 5 minutes to meld the flavors.
Serve the soup hot, with a generous scoop of shredded chicken and a hearty spoonful of rice in each bowl. Enjoy the rich, fragrant broth with tender vegetables and meat.