Add the water, soy sauce, vinegar, mango, and garlic to a food processor or blender and blend until smooth. Transfer the mixture to a bowl, stir in the green onion and set aside.
Pat the chicken thighs dry with paper towels.
Heat the peanut oil in a large saute pan over medium-high heat. When the oil is hot place the chicken skin-side down in the oil and cook until skin is crispy and browned, about 5 minutes. Transfer the chicken to a plate and set aside.
Pour the mango mixture into the pan and use a wooden spoon the scrape the bottom of the pan to release any stuck on bits. Nestle the chicken thighs into the sauce and bring the sauce to a boil.
Reduce the heat to medium-low and place a lid on the pan. Simmer over medium-low until chicken is cooked through, about 35 minutes, flipping the chicken thighs over half-way through.
MAKE THE RICE WHILE THE CHICKEN SIMMERS: Stir together the rice and water in a medium-size saucepan and bring to a boil over medium-high heat. Place a lid on the pan and reduce the heat to low. Simmer, WITHOUT REMOVING THE LID, for 10 minutes. Turn off the heat and let sit, KEEPING THE LID ON, for 15 more minutes.
Take the lid off the pan with the chicken and transfer the chicken thighs to a serving plate. Increase the heat to medium-high and continue to cook the sauce, stirring often, until thickened, about 10 minutes.
Pour the sauce over then chicken thighs then sprinkle with the sesame seeds.
Fluff the rice with a fork and serve with the chicken and sauce.