Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chicken pieces and cook until golden brown and cooked through. Remove and set aside.
In the same skillet, add the remaining olive oil. Add the orzo and cook, stirring frequently, until it begins to brown lightly.
Pour in water as per package instructions for orzo, add oregano, and cook until the orzo is al dente and the water is absorbed.
Stir in the cherry tomatoes and spinach, and cook until the spinach is wilted.
Return the cooked chicken to the skillet, and add lemon juice. Stir everything to combine.
Serve warm, topped with crumbled feta cheese.