In a medium pot, combine water, salt, and soy sauce. Bring to a gentle simmer over medium heat.
Add the chicken breasts and poach for about 15-20 minutes, or until the chicken is cooked through (internal temperature should reach 165°F).
Remove the chicken from the pot and let it rest for 5 minutes before slicing.
While the chicken is resting, prepare the scallion ginger sauce by mixing together the chopped scallions, grated ginger, soy sauce, rice vinegar, and salt in a small bowl.
In a small saucepan, heat the vegetable oil over medium heat until hot but not smoking. Carefully pour the hot oil over the scallion mixture and stir to combine.
Slice the poached chicken and serve it drizzled with the scallion ginger sauce.