Thinly slice the squash lengthwise on a mandoline. As you slice, lay the slices on a large platter. Once you cover the plate, lightly sprinkle the squash with some chives and about 1 teaspoon olive oil.
Cut into the lemon about halfway so you can squeeze the juice but still grate off the zest. Finely grate about 1/4 teaspoon of the lemon zest and squeeze 4 or 5 drops of juice over the squash. Top with a sprinkling of tarragon, about 1 teaspoon. Keep it light because the flavor adds up as you layer the vegetables. Season evenly with salt and pepper. Repeat with the ingredients to make 4 or 5 layers of squash flavored with the herbs, lemon and olive oil. Finish with a nice drizzle of the olive oil and herbs.
Set aside to allow the squash to soften slightly, about 30 minutes. Lay the slices of cheese on top. Serve.