Recipe(tried): Chicken in Champagne Sauce

I made this for my husband and myself last year. It's from True Grits cookbook and it was good. The champagne wasn't expensive to use. I serve rice with it to use the sauce.

Breasts of Chicken in Champagne Sauce
serves 6

6 chicken breast, boneless, skinless
1 tablespoon paprika
salt
white pepper
1 whole lemon juice
2 teaspoons shallots, chopped
1/4 cup butter
2 cups Champagne, extra dry
4 cups cream
2 bunches green onions including tops, chopped

Rinse the chicken and pat dry. Sprinkle both sides with the paprika, salt and white pepper. Place in a saucepan. Add the lemon juice, shallot, butter and Champagne. Mix well.
Poach, covered, for 10 minutes or until the chicken is cooked through. Remove the chicken with a slotted spoon to a platter.
Cook the pan juices until reduced by 2/3, stirring constantly. Stir in the cream. Cook until the liquid is reduced by 1/2, stirring constantly. Add the chicken, mix well.
Cook just until the chicken is heated through, stirring occasionally.
Arrange the chicken on a serving platter, drizzle with the sauce. Sprinkle with the green onions.