While the hot-water tap runs, put the rice in a 2-quart saucepan. Add 2 cups hot tap water and 1 teaspoon salt. Bring to a boil over high heat, then reduce the heat to low, cover, and cook for 10 minutes. Turn off the heat and keep covered until ready to serve. (Or put the rice, 2 cups hot tap water, and 1 teaspoon salt in a 2-quart microwave-safe container. Cover and cook in a microwave oven on high power for 10 minutes. Keep covered until ready to serve.)
Put the oil in a large, heavy skillet over medium-high heat. Cut the chicken into 1-inch pieces. Raise the heat to high and add the chicken. Peel and halve the ginger. Drop the ginger down the chute of a food processor with the motor running. While it purées, peel and quarter the onion. Add it to the processor and pulse just until chopped. Add the ginger and onion to the skillet and stir. Add the curry, cayenne, and salt to taste. Cook for 2 minutes, stirring occasionally. Add the coconut milk, stir, and bring to a boil. Continue cooking, uncovered, for about 5 minutes, or until slightly thickened.
Meanwhile, place each mango, narrow side down, on a cutting surface. Slice through the mango as close to the pit as possible on one side, then repeat on the other side. With a teaspoon, scoop out the flesh from the two thick slices and cut into bite-size pieces. Peel the banana and cut crosswise into 3/4-inch-thick slices. Peel the kiwis and halve lengthwise, then cut each half crosswise into 4 half-moon slices. Add the fruit to the chicken and stir gently. Cook for 1 to 2 minutes, only until the fruit is heated through but still maintains its shape. Serve over the rice.