Snap off tough lower parts of asparagus stems. Cut remaining asparagus into 1/2" pieces.
Melt butter in a 4-quart heavy pot over moderately low heat. Add chopped onion and cook, stirring, until softened.
Add asparagus pieces, salt and pepper to taste. Cook, stirring, 5 minutes.
Add broth and simmer, covered, until asparagus is very tender, 15 to 20 minutes.
Add soup in batches to a blender, along with chives, reserving a few stems for garnish. Pur�e soup until desired consistency.
Return to pan. Mix a small amount of soup into the cr�me fra�che to eliminate lumps. Add the cr�me fra�che mixture to the sop. If the soup is thicker than desired, a little more broth may be added. Season with salt and pepper.
Heat soup without boiling.
Garnish with a swirl of cr�me fra�che and a sprig of chive.