In a medium pot, bring water, salt and rice to a boil. Once boiling, cover the pot with a lid and reduce to low and allow to simmer. Cook 15-20 minutes, until water is evaporated and rice is tender. Fluff with a fork and set aside.
While the rice is cooking, make the teriyaki sauce. In a small pot, combine tamari sauce, water, honey, ginger and garlic. Cook over medium heat for 3-5 minutes. Meanwhile, combine cornstarch with two tablespoons of water in a small bowl and whisk until there are no lumps from the cornstarch. Stir the cornstarch mixture into the pot with the tamari. Whisk to combine. Heat until the sauce thickens.
To make the stir-fry, heat a large skillet or wok over medium heat and add one tablespoon of the oil.
Add onions, bell peppers, broccoli and snap peas. Cook for 5-7 minutes, until vegetables are slightly browned and tender. Remove with a slotted spoon and set aside on a large plate or bowl.
Add another tablespoon of oil to the pan. Add chicken pieces to the skillet and cook for 8-10 minutes, until chicken is browned and cooked through.
Add back the vegetables and stir in the teriyaki sauce.
Serve with cooked rice and top with green onions.