Preheat oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Slice the bell peppers into 1-inch wide strips, removing the seeds and stems.
Pat the chicken breast dry with a paper towel and season both sides with half of the sea salt, black pepper, and dried oregano.
Place the chicken and peppers on the prepared sheet, drizzle with olive oil, and toss the peppers to ensure they are well-coated.
Roast for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the peppers are tender with charred edges.
Transfer the chicken to a cutting board and let it rest for 5 minutes to keep it juicy before slicing into thin strips.
In a large mixing bowl, combine the fresh arugula and the warm roasted bell peppers.
Add the sliced chicken, crumbled feta cheese, balsamic vinegar, and the remaining seasonings.
Toss everything together gently so the feta slightly softens from the heat of the chicken and peppers, then serve immediately.