To a 6-quart slow cooker, add the onion, carrot, celery, potato, diced tomatoes, tomato paste, bay leaf, garlic powder, stock, salt, and chicken, stirring to combine.
Cover and cook on high for 4-5 hours or low for 7-8, until the potatoes are tender and the chicken is cooked through. Do not uncover during this time.
Uncover and add the green beans to the slow cooker, and stir and cover.
Turn off the heat and add the corn and peas, stirring to combine, allowing a minute or two for the vegetables to warm through. Taste and add additional salt if desired.
