Season the chicken breast with half of the salt, pepper, and oregano, then grill over medium heat until cooked through and slice into bite-sized pieces.
Cook the orzo pasta in boiling salted water according to package instructions, drain well, and set aside to cool slightly.
In a large mixing bowl, whisk together the extra virgin olive oil, fresh lemon juice, minced garlic, and the remaining dried oregano, salt, and pepper.
Add the cooked orzo, sliced chicken, halved cherry tomatoes, diced cucumber, minced red onion, and chopped baby spinach to the bowl.
Toss all ingredients thoroughly until the pasta and vegetables are evenly coated with the lemon dressing.
Gently fold in the crumbled feta cheese and serve immediately or refrigerate for an hour to let the flavors meld.