Place the chicken in a large pot. Season with 1 teaspoon salt per pound of chicken. Add the onion, celery, thyme, and garlic. Cover with water, ensuring the chicken is submerged if your pot allows it. You will need 12–14 cups of water to cover the chicken. It’s ok if the very top of the bird is exposed.
Turn the heat on the pot to high and bring to a boil. Cover and reduce the heat to low. Simmer for at least 1 hour 30 minutes or until the chicken is completely cooked.
Using tongs, carefully transfer the chicken to a large bowl and cool for 10-15 minutes.
Turn the heat on the pot to medium-high. Allow the broth to simmer rapidly, uncovered, for 30 minutes, reducing it to 10 cups total. It will deepen in color and flavor. Adjust the heat as needed to keep the broth from reducing too much.