Melt the butter in a small saucepan over low heat. Whisk in the flour to create a smooth roux.
Gradually pour in the heavy cream, whisking constantly to prevent lumps from forming.
Add the salt, white pepper, and lemon juice. Simmer over low heat for 3-4 minutes, or until the sauce has slightly thickened.
Finely chop the fresh chives and stir them into the sauce. Cook for another 1-2 minutes to allow the flavors to meld.
Serve the sauce hot with fish, poultry, or fresh vegetables.
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