In a large, deep skillet, sauté onion in oil until soft, 3-5 minutes.
Add thyme, bay leaf and 3 c water. Bring to a simmer, reduce heat to low and add chicken. Poach until cooked through 15-20 minutes. Remove chicken from water, pat dry and use two forks to shred.
In a saucepan of water add 1 T salt, carrots and potatoes and cook until tender, 10-12 minutes. Add peas and raisins, cook 1 minute, then drain.
In large bowl whisk Chobani, mayonnaise, mustard, vinegar, and ¾ t salt. Stir in chicken, carrots, potatoes and peas and serve.