In 2-quart saucepan, heat rice and water to boiling on high.
Reduce heat to maintain simmer; cover and cook 20 minutes.
Remove from heat.
Let stand 5 minutes, covered.
Fluff with fork; cool completely.
Meanwhile, in 1-quart saucepan, heat soy sauce, sugar, and 2 teaspoons vinegar to simmering on medium-high, stirring.
Reduce heat to simmer 1 to 2 minutes or until slightly reduced.
Sprinkle chicken with 1/4 teaspoon pepper; grill, covered, 25 minutes, turning over once.
Brush soy mixture over chicken; grill, uncovered, 5 to 6 minutes, until instant-read thermometer inserted in thickest part reads 165 degrees F, turning and brushing with soy mixture frequently.
In large bowl, whisk mayonnaise, remaining 2 tablespoons vinegar, oil, hot sauce, and 1/4 teaspoon salt until blended.
Add broccoli, radishes, red onion, and cooled rice; stir to combine.