Method:
In a medium bowl, whisk together 3/4 cup coconut milk, 2 tablespoons lime juice, ginger, tamari, 2 teaspoons sugar and hot sauce. Transfer 1/4 cup of the mixture to a small bowl and set aside. Add chicken to bowl with remaining marinade and refrigerate for at least 2 hours or overnight.
Add peanut butter to 1/4 cup mixture in small bowl and whisk until smooth. Place cucumber, carrot, remaining 2 tablespoons lime juice, remaining 1 teaspoon sugar, cilantro and salt in a medium bowl and toss until combined. Refrigerate peanut sauce, cucumber salad and remaining coconut milk until ready to serve.
When ready to cook, place rice, remaining 1 cup coconut milk and 1 1/4 cups water in a medium saucepan and heat to a boil over medium-high heat. Cover, reduce to a simmer and cook 45 minutes or until all liquid is absorbed. Fluff with a fork.
While rice cooks, thread chicken onto skewers and discard marinade. Preheat grill to medium heat. Cook chicken until cooked through, about 4 minutes on each side. Serve with peanut sauce, cucumber salad and rice.