Melt 1 tablespoon butter in a large stockpot or Dutch oven over medium high heat heat. Season chicken with salt and pepper, to taste. Add chicken to the stockpot and cook until golden, about 2-3 minutes; set aside.
Reduce heat to medium; melt remaining 4 tablespoons butter. Add onion, carrots and celery. Cook, stirring occasionally, until tender, about 3-4 minutes. Stir in garlic and poultry seasoning until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute.
Stir in wine, scraping any browned bits from the bottom of the stockpot.
Stir in chicken stock and bay leaf. Bring to a boil; reduce heat and simmer until flavors have blended, about 10-12 minutes.
Stir in green beans, heavy cream and chicken; simmer until green beans are tender and soup has thickened, about 3-4 minutes.
Stir in parsley and vinegar; season with salt and pepper, to taste.