Drizzle some olive oil in a heavy pot over medium-high heat. Season the chicken breasts with salt and pepper. Fry the chicken on both sides until fully cooked through, about 4 minutes per side. Set aside.
Add the carrots, celery, onion and garlic to the pot and cook, stirring. Sprinkle over the thyme and 1/2 teaspoon black pepper. Reduce the heat to low and cook the veggies slowly, 3 to 4 minutes.
Dice the chicken into very small pieces, then add them to the pot. Add the broth, bouillon cubes and 2 cups water and raise the heat to bring it to a gentle boil. Simmer for 10 minutes. Turn off the heat and stir in the noodles.
Serve piping hot with a sprinkling of parsley over each bowl.