Season the chicken breast evenly on both sides with the sea salt, black pepper, and dried oregano.
Heat a large cast-iron skillet over medium-high heat and add half of the olive oil.
Place the chicken in the skillet and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F.
Remove the chicken from the pan and let it rest for 5 minutes before slicing into strips.
While the chicken rests, add the sliced bell peppers to the same hot skillet and sear for 4-5 minutes until they are tender and develop dark charred edges.
In a small bowl, whisk together the remaining olive oil, lemon juice, and minced garlic to create the dressing.
In a large bowl, combine the arugula, halved cherry tomatoes, and charred bell peppers.
Drizzle the dressing over the vegetables and toss gently to coat.
Top the salad with the sliced chicken and fresh avocado slices before serving.