Add the cucumber slices to the water and refrigerate to infuse.
Pat the chicken dry. Rub with 1 tsp of olive oil, half of the dried oregano, salt, and black pepper. Let the chicken marinate while preparing the remaining ingredients.
In a large bowl, whisk together the lemon juice, remaining olive oil, garlic, and remaining oregano until well combined.
Add the cannellini beans to the dressing and toss to coat. Let the beans marinate for 10 minutes.
Heat a grill pan or skillet over medium-high heat. Grill the chicken on both sides until the internal temperature reaches 165°F (74°C). Let rest for 5 minutes before slicing.
In a bowl, combine the cherry tomatoes, cucumber, red onion, parsley, and Kalamata olives. Add the marinated beans along with any remaining dressing and toss gently to combine.
Portion the bean and vegetable mixture into bowls. Top with sliced grilled chicken and sprinkle with crumbled feta cheese.
Serve the White Bean Chicken Bowl with cucumber water over ice if desired.