Toast orzo in a dry skillet over medium high until golden, 3-5 minutes and transfer to a bowl.
Pat chicken dry and season lightly with salt and pepper
Heat one teaspoon oil in skillet on medium high heat and brown chicken lightly, 3-4 minutes per side and transfer to a plate.
Add remaining 2 teaspoons of oil to skillet and cook garlic, oregano and red pepper flakes until fragrant, about 30 seconds. Stir in broth and toasted orzo.
Nestle chicken pieces into the skillet mix, lower heat to medium low and simmer until it registers 160, approximately 10 minutes.
Move chicken to a serving platter
Continue to cook orzo stirring in additional broth 1 tablespoon at a time until soft and creamy.
Stir in spinach, cook until wilted and then stir in feta cheese and lemon juice.
Serve the chicken on top of the orzo spinach mix.