Melt butter in 4-quart saucepan until sizzling; add chicken and onion. Cook over medium-high heat, stirring occasionally, until onion is softened (2 to 3 minutes).
Add water, carrots and potatoes. Continue cooking, stirring occasionally, until mixture comes to a boil (4 to 6 minutes). Add all remaining ingredients. Reduce heat to medium. Continue cooking until vegetables are tender (12 to 15 minutes).