For the poached chicken:
Place the chicken in a medium stockpot, adding enough water to just cover the chicken. Stir in the vinegar, sugar, peppercorns, bay leaves, and kosher salt.
Gently simmer over medium heat until the chicken is cooked through, about 45 minutes. Cooking time will vary depending on the thickness of the chicken breasts. Turn off heat and leave the chicken in the cooking liquid for an additional 10 minutes.
Transfer the chicken to a bowl and allow it to cool enough to handle.
For the chicken salad:
In a large bowl combine the shredded chicken, cucumbers, olives and mayonnaise along with the olive juice. Add ½ teaspoon of the kosher salt, and pepper, stirring to mix well. Add the remaining kosher salt if needed.
Cover and refrigerate overnight before serving.