In a large pot, combine the chicken pieces, water, salt, and pepper. Bring to a boil over medium-high heat.

Reduce heat to low and simmer for about 30 minutes, skimming off any foam that rises to the surface.

Add the carrots, celery, onion, and garlic to the pot. Stir in the thyme, parsley, and bay leaf.

Continue to simmer for an additional 15 minutes, or until the vegetables are tender.

Remove the chicken from the pot and let it cool slightly. Shred the meat from the bones and return it to the pot.

Add the peas and simmer for another 5 minutes. Adjust seasoning if necessary.

Serve hot, garnished with fresh parsley if desired.