In a large bowl, stir together chicken, grapes, mayonnaise, almonds, celery, tarragon, and pepper.
Spread chicken salad in a thick layer onto 4 bread slices. Cover with remaining bread slices.
Using a serrated bread knife in a gentle sawing motion, trim and discard crusts from sandwiches, creating squares. Cut sandwiches diagonally into quarters, creating 4 triangles.
Serve immediately, or cover with damp paper towels, place in a covered container, and refrigerate for a few hours until serving time.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/green-grape-chicken-salad-tea-sandwiches/