Pat the chicken breast dry with paper towels and season both sides with half of the sea salt and black pepper.
Heat the olive oil in a medium skillet over medium-high heat until shimmering.
Add the chicken to the skillet and sear for 6-7 minutes per side, or until the internal temperature reaches 165 degrees Fahrenheit.
While the chicken cooks, peel the cucumber partially to create a striped pattern, then slice it into thin rounds.
In a medium mixing bowl, whisk together the Greek yogurt, minced garlic, lemon juice, chopped fresh dill, and the remaining salt and pepper.
Gently fold the cucumber slices into the yogurt mixture until every slice is thoroughly coated.
Remove the chicken from the heat and let it rest for 3 minutes before slicing it into strips.
Plate the chilled cucumber yogurt salad alongside the warm seared chicken and garnish with extra dill if desired.