Place chicken breast between two sheets of plastic wrap or wax paper and pound with a meat mallet to about a 1/2 inch thickness. Season both sides of breast with dried tarragon, salt and pepper, set aside.
In a large skillet over medium high heat, add a tablespoon of oil, such as olive or coconut. Sauté chicken breast until lightly browned on both sides and juices run clear, about 2 minutes per side. Transfer chicken breast to a plate, cover loosely with foil.
Trim away dark green leaves and root end of leek. Split leek in half lengthwise and rinse under running water, separating layers, to wash away any dirt.
In the same skillet over medium heat, add remaining tablespoon of oil. Place leek halves cut side down in skillet and sauté for 5 minutes. Add water or chicken broth to skillet, cover and cook until leeks are tender and nicely caramelized, about 15 minutes. Transfer leeks to platter with chicken breast.
Add unsweetened coconut milk to skillet, scraping brown bits from bottom of pan with a wooden spoon. Simmer until sauce has heated through, about 2 minutes, then season with salt and pepper to taste. Pour sauce over chicken breast and leek halves. Garnish dish with fresh tarragon, serve immediately.
If you don't have a meat mallet, you can use the flat bottom of a small skillet or saucepan to pound the chicken breast.
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