In a medium glass bowl, whisk together the Greek yogurt, 1 tablespoon of lemon juice, dried oregano, garlic powder, sea salt, and black pepper.
Place the chicken breast in the bowl and coat thoroughly with the yogurt marinade; cover and refrigerate for at least 15 minutes.
While the chicken marinates, prepare the salad by combining the sliced cucumber, thinly sliced red onion, and chopped fresh dill in a small bowl.
Whisk together 0.5 tablespoon of lemon juice and 0.5 tablespoon of olive oil, then pour over the cucumber mixture and toss to coat.
Heat the remaining 1 tablespoon of olive oil in a cast-iron skillet over medium-high heat until shimmering.
Remove the chicken from the marinade, allowing excess to drip off, and place in the hot skillet.
Sear the chicken for 5 to 6 minutes per side until the internal temperature reaches 165 degrees and a golden crust has formed.
Let the chicken rest for 3 minutes before slicing it into strips and serving alongside the chilled cucumber salad.