Prepare all the ingredients as instructed.
Add cucumber slices to water and refrigerate to infuse.
Prepare the marinade. In a small bowl, combine the olive oil, lemon juice, minced garlic, oregano, parsley, dill, salt, and black pepper.
Marinate the chicken. Add the chicken and coat thoroughly with the marinade. Cover and refrigerate for 20–30 minutes.
While the chicken marinates, cook the Gigandes Skordati: Heat the olive oil in a skillet over medium-low heat. Add the red onion and cook for 4–5 minutes, stirring occasionally, until softened.
Stir in the garlic and cook for 1 minute until fragrant. Avoid browning the garlic.
Stir in the beans and water. Simmer over low heat for 8–10 minutes, stirring gently, until heated through. Lightly mash a few beans to create a creamier sauce, if desired.
Preheat the grill to medium heat.
Remove the chicken from the marinade and discard the marinade. Grill the chicken on both sides to an internal temperature of 165°F (74°C). Set aside and rest for 5 minutes before slicing.
Remove the beans from the heat. Stir in the lemon juice, fresh dill, and parsley. Taste and adjust the lemon juice as desired.
Toast the bread until golden.
Serve the chicken alongside Gigandes Skordati, bread, and cucumber water.