Cook the pasta according to the package directions. Reserve 1 cup of the cooking water; drain.
Meanwhile, heat 2 tablespoons of the butter in a medium skillet over medium-high heat. Add the leeks and ¼ teaspoon each salt and pepper. Cook, stirring occasionally, until tender, 2 to 4 minutes.
Add the pasta, chicken, Dijon, the remaining 2 tablespoons of butter, and ¾ cup of the cooking water to the leeks and toss to coat (adding more cooking water as needed to loosen the sauce). Add the romaine and toss to combine.
Serve warm, topped with the tarragon.
Edible, but nothing great. What's the point of the romaine?