Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Season the chicken pieces with salt and black pepper.
Add the chicken to the skillet and sear until golden brown on all sides, about 5 to 7 minutes. Remove the chicken and set it aside.
In the same skillet, add the minced garlic and cook for 1 minute until fragrant. Stir in the dry orzo, toasting it slightly for 1 to 2 minutes.
Pour in the chicken broth, scraping up any browned bits from the bottom of the pan. Bring to a simmer, cover, and cook for 8 to 10 minutes, or until the orzo is mostly tender.
Stir in the heavy cream, lemon juice, lemon zest, and cooked chicken. Simmer uncovered for 2 to 3 minutes until the sauce thickens slightly.
Remove from heat and fold in the fresh spinach until wilted. Serve immediately.