Preheat oven to 180°C (350°F). Season chicken inside and out with salt and pepper.
In a large ovensafe pot or Dutch oven, heat oil on medium-high. Add chicken and brown, breast side down, for 5 to 10 minutes. Turn over and brown second side. Transfer chicken to a platter. Add celery and onion to pot and sauté for 5 minutes. Add carrots and sauté for another 5 minutes. Remove from heat.
Place chicken, breast side down, overtop vegetables in pot. Combine broth, water and vinegar and pour over chicken. Add potatoes, cover, and braise in oven for 45 minutes. Turn chicken, breast side up, and cook another 10 to 15 minutes with lid off to brown. Cook until a meat thermometer inserted in meatiest part of the thigh reads 82°C (180°F).
Remove chicken and vegetables from pot and keep warm. Skim fat from cooking liquid and discard.
Carve chicken and place slices into shallow bowls, adding vegetables and broth. Garnish with fresh chives and serve.