Season the chicken breast evenly on both sides with sea salt, black pepper, and dried oregano.
Preheat a grill or grill pan over medium-high heat and lightly grease with a small amount of oil to prevent sticking.
Grill the chicken for 5 to 7 minutes per side until the internal temperature reaches 165 degrees Fahrenheit, then set aside to rest for 5 minutes.
While the chicken rests, slice the peach into thick wedges and place them on the grill for 1 to 2 minutes per side until lightly charred and softened.
In a small jar or bowl, whisk together the extra virgin olive oil and balsamic vinegar until well emulsified.
In a large serving bowl, combine the arugula, thinly sliced red onion, and pecans.
Slice the rested chicken into strips and arrange them over the greens along with the warm, charred peach wedges.
Drizzle the balsamic dressing over the top and toss gently before serving.