Combine 1st 6 ingredients in a medium saucepan and bring to a boil.
Add shrimp; reduce heat to low, cover and poach until shells are pink and shrimp have opaque centers (3-4 min).
Use slotted spoon to transfer shrimp to ice bath, reserve poaching liquid. Drain & peel shrimp, leaving tails intact, and devein.
For dipping sauce, boil remaining poaching liquid until reduced to 2-3 T (about 20 mins), then strain and cool.
Mix crème fraiche, chopped chives, horseradish and 1 T of reduced poached liquid in a small bowl and season to taste with salt & pepper. (Shrimp & sauce can be made 1 day ahead; cover separately then chill.
Spoon dipping sauce into short glasses. Arrange shrimp on rims, garnish with whole chives.