Trim 3 bunches asparagus; peel the bottoms. Boil until tender, 4 to 5 minutes; drain and cool. Peel the cloves from 4 heads garlic and cook in 1/2 cup olive oil over low heat until soft, 30 minutes. Drain, reserving the oil. Puree the garlic with 2 tablespoons lemon juice, 1 teaspoon mayonnaise, 1 1/2 teaspoons sugar, 1 teaspoon dijon mustard and 1/4 cup water. Blend in 1/4 cup of the garlic oil. Season with salt, pepper and chopped chives; serve with the asparagus.