Combine soy sauce, lime juice, water and cornstarch in a small bowl, mix together and set aside.
Season chicken lightly with salt. Heat a large wok over high heat. When the wok is very hot, add half of the oil, then add the chicken. Stir fry, stirring occasionally until the chicken is cooked through and browned, about 3-4 minutes. With a slotted spoon, remove the chicken and set aside. Reduce heat to medium.
Add the remaining oil to the wok; add the garlic and ginger, stir for 20 seconds. Add the sugar snap peas and carrots, stirring over medium high heat until tender crisp, about 3-4 minutes.
Return the chicken to the wok, add the soy sauce-lime mixture, mix well and cook another 30 seconds to one minute. Serve immediately and top with fresh scallions.