In a medium pot, bring about 5 cups water (enough water to submerge the chicken breast) to a boil over high heat along with the ginger slices and scallion.
Once boiling, lower the chicken breast into the pot. Bring back to a boil (stay close to the stove, as it will happen very fast).
Once the water is boiling again, immediately reduce the heat to the lowest setting, cover, and simmer for 3-5 minutes, depending on the size and thickness of your chicken breast.
After 3-5 minutes, turn off the heat and let the pot stand on the stove (still covered) for 10-15 minutes to continue cooking.
To test if the chicken is cooked, pierce the thickest part of the chicken to make sure the juices run clear, not cloudy in the poaching water.
Transfer the chicken to a bowl of cold water for 5 minutes to stop the cooking process and lock in the juices. Drain and slice right before serving. Slice the chicken against the grain (i.e., across the breast so you get short pieces) to get the best texture.