Remember bowls of ramen in college, this dish is nothing like those. Instead, this is a sophisticated and satisfying meal. Slideshow: Best Noodle Dishes
Season the chicken with 3/4 teaspoon salt and 1/2 teaspoon pepper. In a medium pot, heat the oil over medium high heat until hot. Brown the chicken, turning once, until golden, then transfer to a plate. Stir in the shallots, garlic, and ginger with 1/2 teaspoon salt, and cook, stirring occasionally, until browned, 5 to 6 minutes. Add the chicken back to the pot along with any accumulated juices. Stir in the coconut milk and stock and bring to a boil. Reduce the heat and simmer, covered, 20 minutes. Stir in the ramen and continue to boil, covered, until the chicken is cooked through, about 5 minutes more. Season with salt and pepper to taste.
Serve the chicken with the broth and ramen, sprinkled with the cilantro leaves and chile slices and drizzled with the lime juice.