Trim the ends off the leeks, leaving 0.5-inch of green. Slice the leeks in half lengthwise then wash to remove any dirt, sand, or rocks that may be hiding between the layers. Cut into 0.5-inch slices and set aside.
Season the chicken thighs all over with salt and pepper.
Heat an oven-proof skillet over medium-high heat. When hot, add the oil. Once the oil starts to shimmer add the chicken thighs skin-side down and cook until brown (5 to 6 minutes), flip and cook the other side for and additional 5 minutes. Remove the chicken from the skillet and set aside.
Remove all but a thin layer of fat from the skillet. Reduce heat to medium and add the leeks and garlic. Cook, stirring frequently, until they begin to brown, about 6 to 8 minutes.
Add the chicken stock and Riesling and bring to a boil, scraping the bottom of the pan with a wooden turner to remove any stuck-on bits.
Return the chicken to the skillet and place in the oven. Bake, uncovered, until the chicken is cooked through (165 degrees) about 20 to 25 minutes.