Heat the butter in a large pan over medium heat. Add the garlic and cook, stirring constantly until it softens and begins to turn a very light golden color. Be careful not to allow it to crisp or brown. Add the flour, and continue stirring until it is well incorporated into the butter and garlic. Continue cooking, stirring constantly, until the flour begins to turn golden yellow.

Gradually begin stirring in the chicken broth, blending it with the flour mixture until the sauce is smooth, creamy and thickened. Add the salt and pepper, taste and adjust the seasoning if necessary. Whisk in the sour cream and blend until smooth. Add the fresh chives just before serving.