Using a small, sharp knife, cut between the membranes of the grapefruit, releasing the segments into a small bowl.
In a medium bowl, combine the crabmeat, mayonnaise, lemon juice, tarragon, chives, Tabasco and salt. Cut the avocados in half, remove the pits and gently scoop the meat out of the shells, keeping the shape intact. Cut each avocado half into thin slices, still keeping the shape, then mound some crab salad where the pits used to be. Wrap each serving tightly with plastic wrap, twisting the end of the wrap to form a tight ball. Unwrap and garnish with grapefruit segments.