In large saucepan, bring 2-1/2 cups (625 mL) water to boil; add rice and return to boil. Cover and reduce heat to low; simmer until no liquid remains, 12 minutes. With fork, gently stir twice. Remove from heat; let stand, covered, for 10 minutes.
Chicken and Egg: Meanwhile, cut chicken into bite-size cubes. In nonstick skillet, heat oil over medium-high heat; sauté chicken and onion until browned, about 5 minutes.
In measuring cup, whisk stock, soy sauce, mirin and sugar; pour into skillet and bring to boil. Cover and simmer until thickened slightly and chicken is no longer pink inside, 5 minutes.
In thin stream, pour in eggs; sprinkle with half of the green onions. Cover and cook until egg is set, 2 minutes. Divide rice among 4 soup bowls. Top with egg mixture; sprinkle with remaining onions.