Preheat the oven to fan 180C/conventional 200C/gas 6. Make a slit down the centre of each chicken breast with a sharp knife (taking care not to cut right through) then open up the slit with your fingers to make a pocket. Arrange the chicken in a single layer in a large, lightly oiled ovenproof dish.
Reserve 8 sprigs of tarragon, chop the rest of the leaves and beat into the cheese with plenty of ground black pepper. Spoon into the pockets in the chicken. Slice the tomatoes and place 2 slices over each cheese-filled pocket. Put a sprig of tarragon on top and drizzle with oil.
Season and bake for 25-30 minutes until the chicken is cooked, but still moist. If serving cold, pour off the juices otherwise they will set to a jelly once cold.
Transport in the dish covered with cling film. You can prepare up to step 3 and serve cold, or cook when you get there.