Peel the lemongrass until you reach the tough inner white bulb. Mince.
Season the chicken with salt and pepper. Heat oil in a large pot over medium-high heat. Cook the chicken until golden brown (approximately eight minutes). Set the chicken aside.
Add the coconut milk to the pot, and bring to a boil. Cook over medium-high heat until reduced to about three cups (approximately 15 minutes).
Stir in the curry paste, and simmer for an additional five minutes.
Return the chicken to the pot along with any juices. Add the lemongrass, lime zest, chicken stock, and fish sauce. Partially cover, and simmer over low heat for 30 minutes.
Add the poblano, cilantro, and basil. Cook, uncovered, for an additional 10 minutes.