Bring a large pot of salted water to a boil, add the orzo, and cook according to package directions; drain and return to the pot.
While the orzo cooks, heat 3 tablespoons olive oil in a large skillet over medium heat.
Add the diced Vidalia onion to the skillet and cook, stirring occasionally, about 3 minutes until softened.
Add the diced chicken to the skillet, season with kosher salt and black pepper, then sprinkle with Italian seasoning and dried oregano; cook, stirring and flipping frequently, about 5 minutes or until the chicken is cooked through.
Add the minced garlic to the skillet, stir, and cook about 1 minute until fragrant.
Transfer the cooked chicken, onions, and any pan juices into the pot with the drained orzo and stir to combine.
Add the fresh spinach to the pot and stir for about 2 minutes until it wilts and integrates with the orzo and chicken.
Stir in the diced cucumber, sliced tomatoes, lemon zest, lemon juice, additional salt and pepper to taste, and mix until well combined.
Fold in the crumbled feta; if you prefer larger feta pieces, wait until the mixture has cooled slightly before adding so it doesn't soften completely.
Taste and adjust seasoning, drizzle additional olive oil if desired, and serve immediately warm or let cool to serve chilled.