In a heavy 2-quart saucepan, combine vinegar, wine, shallots, lemon, and bay leaves to make an infusion. Simmer over medium heat for 5 to 8 minutes until the mixture is reduced to a wet paste, about 2 tablespoons. Add the cream and continue to simmer until reduced again to about 2 tablespoons. Cream is added to make the sauce more stable and less likely to separate.
Reduce the heat to low and remove the bay leaves. Whisk in the chunks of butter in small batches. The butter should melt without the sauce getting too hot, producing a creamy emulsified sauce. Do not let the sauce go over 130 degrees F, where it will separate. If the sauce starts to break, remove from heat, add 2 ice cubes and whisk until it cools down and comes back together. Season with salt and pepper, fold in the chives, and serve immediately. Keep covered in a warm place for a few hours, if needed.
Serve with fish or vegetables.
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