Season chicken on both sides with 1/8 teaspoon salt and a pinch of pepper. Heat 2 teaspoons oil in a medium nonstick skillet over medium-high heat. Add the chicken and cook until well-browned on both sides, about 3 minutes per side. Transfer to a plate and cover with foil to keep warm.
Reduce heat to medium and add the remaining 2 teaspoons oil to the pan. Add pear, shallot and curry. Cook, stirring, until softened, 2 to 3 minutes. Add wine and broth; bring to a simmer. Cook until slightly thickened, about 3 minutes.
Return the chicken and any accumulated juices to the pan. Reduce heat and simmer until the chicken is cooked through, 4 to 6 minutes. Transfer the chicken to 2 plates. Add coconut milk, cilantro and mint to the pan and stir to combine. Season with the remaining 1/8 teaspoon salt and pinch of pepper and spoon over the chicken.