Pat the chicken dry and season with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until golden and cooked through, about 5-6 minutes. Remove chicken to a plate.
In the same skillet, add onion and cook until softened, about 3 minutes. Add garlic and cook for 30 seconds until fragrant.
Stir in the orzo and toast for 1-2 minutes, until lightly golden. Pour in the chicken broth and bring to a boil. Reduce heat to medium-low, cover, and simmer for 10-12 minutes, stirring occasionally, until orzo is al dente and most liquid is absorbed.
Stir in the heavy cream, lemon juice, lemon zest, and half the dill. Return the chicken to the skillet along with any juices. If using spinach, add it now and stir until wilted.
Cook for 2-3 minutes until everything is heated through and the sauce has thickened slightly. Stir in the Parmesan cheese until melted.
Taste and adjust seasoning with salt and pepper. Garnish with remaining fresh dill and serve hot.