Preheat your oven to 400°F and wrap the whole beets in aluminum foil, roasting for 45-60 minutes until tender.
Season the chicken breast with sea salt, black pepper, and dried oregano, then grill over medium-high heat for 6-7 minutes per side.
Once the beets are cool enough to handle, rub off the skins under cold water and dice them into bite-sized cubes.
Toast the walnuts in a small dry skillet over medium heat for 2-3 minutes until they become fragrant and lightly golden.
In a small bowl, whisk together the extra virgin olive oil and balsamic vinegar to create a simple, clean dressing.
Place the fresh arugula in a large bowl and toss gently with the balsamic dressing until the leaves are lightly coated.
Slice the grilled chicken breast into thin strips and arrange them over the bed of arugula.
Top the salad with the diced roasted beets, crumbled feta cheese, and toasted walnuts before serving immediately.