Preheat grill to medium-low. In small bowl, combine oil and chives. Evenly brush herb mixture on slices of bread; sprinkle with sea salt.
Place bread slices on grill 30 seconds on each side or until bread slices are nicely marked by grill.
Remove bread slices to cutting board and cut each slice in half diagonally. Spread evenly with herbed cheese; top with thin layer of radish rounds. Sprinkle with additional sea salt and chives, if desired.
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