Combine squash, onion, and chicken broth in a large Dutch oven; bring to a boil. Reduce heat; cover and simmer 15 minutes or until vegetables are tender. Stir in lemon juice, curry powder, salt, and pepper.
Spoon half of squash mixture into container of an electric blender, and process until smooth. Repeat with remaining squash mixture.
Place squash mixture in a large bowl; add half-and-half, stirring well. Cover and chill thoroughly. Spoon soup into chilled serving bowls; garnish with chives.