In a large saucepan, bring the broth, vegetables, wine, thyme, and bay leaf to a boil. Simmer gently for about 30 minutes or until the vegetables are tender. Strain. Keep the vegetables and cooking liquid separately. You should have 750 ml (3 cups) of cooking liquid. If not, add water or chicken broth.
In the same pan, brown the chicken in the butter. Sprinkle with the flour and cook for 1 minute, stirring constantly. Add the cooking juices. Bring to a boil, stirring constantly. Simmer gently for about 5 minutes.
In a bowl, combine the cream, egg yolks and lemon juice. Add a ladle of the warm sauce to the egg mixture, stirring gently to warm up the eggs. Add this mixture to the sauce, whisking vigorously. Add the vegetables and heat thoroughly without boiling, to avoid overcooking the eggs. Adjust the seasoning. Sprinkle with the chives. Serve with long grain white rice.