These butter-flour balls (beurre manie) can be made ahead in advance and stored in a sealed jar in the refrigerator for 1 or 2 weeks.
Combine 1 tb flour and 1 tb sweet butter on a small flat plate and blend the mixture with a fork into a very smooth paste. Roll the paste into a ball.
In a small skillet, heat 2 tb of butter. Add the scallions and cook for 2 or 3 minutes without browning. Add the mushrooms. Season with salt and pepper and cook the mixture over high heat for 2 or 3 more minutes to brown the mushrooms lightly. Reserve.
Season the chicken breasts with salt and pepper and sprinkle them with lemon juice. In a large chicken fryer, melt the remaining butter. When it is quite hot, add the chicken breasts and cook them for 1 minute on each side. Cover the pan with buttered wax paper and then the pan lid.
Lower the heat and simmer the chicken breasts for another 8 to 1 minutes or until the juices run out pale yellow when pierced with a fork. Do not overcook or pierce every piece. Immediately remove the chicken breasts to a serving platter.
Pour the chicken stock into the fryer, raise the heat and reduce the stock until it is almost a glaze. Add the heavy cream and continue cooking over high heat.
Add the Beurre Manie and cook until the sauce heavily coats a spoon. Add the mushroom & scallion mixture. Add the chives and correct the seasoning. Pour the sauce over the chicken breasts and serve at once.