Season the chicken lightly with salt and pepper. In a large pot, heat the olive oil over medium heat.
Add the chicken pieces and brown on all sides, about 4-5 minutes. Remove and set aside.
In the same pot, add the onion, carrot, celery, and garlic. Sauté until the vegetables start to soften and become fragrant, 4-6 minutes.
Pour in the chicken broth, scraping up any brown bits from the bottom of the pot. Add thyme and bay leaf; bring to a gentle simmer.
Return the chicken to the pot. Simmer until the chicken is cooked through, about 8-10 minutes. Remove chicken, chop into bite-sized pieces, and return to the pot.
Stir in the gnocchi and simmer according to the package directions, typically 2-4 minutes, until they float to the top and are tender.
Reduce the heat to low and stir in the heavy cream. Add the spinach and cook just until wilted, about 1-2 minutes. Remove the thyme sprig and bay leaf.
Taste and adjust salt and pepper as needed. Serve warm with crusty bread or a light side salad.