Heat the olive oil in a large Dutch oven or lidded saucepan over medium-high heat. Sprinkle the chicken pieces with salt and pepper. When the oil is shimmering, add the chicken, skin-side down, and sear, without moving, until the pieces pull away easily from the bottom of the pan, 5 to 7 minutes. Flip the chicken and cook two minutes more. If your pot is crowded, remove the chicken to plate (this was necessary for me), and then add the leeks, garlic, ginger, lemon zest, 1 teaspoon of salt and 1/2 teaspoon pepper, stirring to incorporate. Cook for 3 minutes, then add the broth, coconut milk, and tarragon. Return the chicken to the pot if you removed it and bring to a simmer.