Add the olive oil to a large pot over medium high heat, and season the chicken with salt (1 teaspoon). Once the pot is hot, sear the chicken on one side for 3 minutes, flip, and sear for another 3 minutes on the other side, until golden brown. Set aside.
Add the onion, carrot, celery, and garlic to the pot, and saute until the onions are translucent and veggies start to soften.
Pour the flour over the veggies, toss to combine, then add in the broth, 1 cup at a time, stirring continuously to dissolve the flour. Once all of the broth is in, add the wild rice and thyme and return the chicken to the pot.
Bring the soup to a simmer, then cover and let simmer for 50 minutes, scraping the bottom of the pan every 5 minutes to make sure nothing is sticking. Test the rice for doneness. Pull chicken out, shred it, and return back to the soup.
Stir in the cream, lemon juice, and pepper, and taste for salt. Garnish with additional thyme, serve, and enjoy!