Remove and reserve the asparagus tips. Slice the remaining asparagus into 1-inch pieces.
Melt the butter in a large saucepan over medium heat. Add the onion and cook on medium-low to low heat for 5 minutes or until the onion is tender, stirring frequently. Add the sliced asparagus, chicken broth, rice and salt. Bring to a boil. Reduce the heat to low. Simmer for 20 minutes or until the asparagus and rice are tender, stirring occasionally. Pour the soup into a large bowl and cool to room temperature.
Meanwhile, cook the asparagus tips in boiling water for 1 minute or until the color turns bright green. Drain and cool under cold running water and reserve.
Puree the cooled soup with the sour cream in batches in blender until smooth.
Serve at room temperature or heat over medium heat until hot (do not let boil). Garnish with additional sour cream, the asparagus tips and freshly ground pepper.