In a large pot or Dutch oven, melt butter over medium-high heat.
Add chicken pieces and cook until browned on all sides, about 5-7 minutes. Remove chicken and set aside.
In the same pot, add onion, carrots, and celery. Sauté for 5 minutes until vegetables begin to soften.
Stir in garlic and thyme, cooking for 1 minute until fragrant.
Whisk in flour and cook for 1-2 minutes to toast the roux.
Gradually pour in chicken broth while whisking constantly to prevent lumps.
Bring the mixture to a simmer and return the chicken to the pot.
Add the gnocchi and cook for 3-5 minutes, or until the gnocchi are tender and have floated to the surface.
Stir in the heavy cream and frozen peas. Simmer for 2 minutes until the sauce has thickened and peas are heated through.
Season with salt and pepper. Serve immediately.