1. Shuck oysters, reserving oyster liquid. Strain oyster liquid through a sieve over a large saucepan. Pick over oysters to remove any bits of shell. Chill oysters.
2. Add stock and next 5 ingredients (through pepper) to oyster liquid; bring to a simmer. Cover and simmer 20 minutes or until vegetables are tender. Place half of stock mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Pour into a large bowl. Repeat procedure with remaining stock mixture.
3. Return pureed soup to saucepan; bring to a simmer. Stir in half-and-half and oysters; simmer 2 minutes or until oyster edges curl; stir in chives.