Preheat the oven to 350 degrees F.
Using a 1 1/2-inch round cutter, cut 4 rounds from each slice of bread. Place the rounds on a sheet pan and toast in the oven until golden brown, 12 to 14 minutes.
Bring a 5-quart pot of highly salted water to a boil. Prepare a medium bowl with ice and water. Add the shrimp to the boiling water and simmer until cooked through, 3 to 4 minutes. With a slotted spoon or strainer, transfer the shrimp to the ice water to stop the cooking. Drain, pat dry, cut lengthwise and keep cool.
Pulse the creme fraiche with the horseradish in a food processor until smooth. Season with salt.
Place 1 teaspoon of the creme fraiche mixture on 1 toasted round. Top with 1 shrimp and garnish with chopped chives.
BYOC: Need a little extra spice in your life? Try adding your favorite hot sauce to the horseradish mixture. This is a great cocktail party item. You can make all the parts ahead of time and put together right before your guests arrive.