Season the chicken breast evenly on both sides with half of the sea salt, black pepper, and dried oregano.
Heat 0.5 tablespoon of olive oil in a medium skillet over medium-high heat.
Place the chicken in the skillet and cook for 6 to 7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
While the chicken cooks, prepare the dressing by whisking together the remaining 1 tablespoon of olive oil, lemon juice, and the rest of the salt, pepper, and oregano in a small bowl.
In a large salad bowl, combine the mixed baby greens, sliced cucumber, halved cherry tomatoes, and thinly sliced red onion.
Remove the chicken from the pan and let it rest for 3 minutes before slicing into thin strips.
Top the garden salad with the sliced chicken and drizzle the lemon vinaigrette over the top just before serving.