Heat oil in a 5-quart Dutch oven over medium-high heat. Add chicken, salt and pepper and cook for 5 minutes, stirring occasionally.
Add shallot and cook for 2 minutes, then stir in garlic and orzo for 1 minute.
Pour in broth, scrape the bottom and bring to a simmer. Cook uncovered over medium-low heat for 10 to 12 minutes, stirring often and adding reserved water a little at a time if the orzo sticks before becoming tender.
Fold in spinach and cook for 2 minutes until wilted. Check that chicken reaches 165°F and the orzo is tender in a thick, flowing sauce.
Remove from the heat and stir in lemon zest, lemon juice and feta. Rest for 2 minutes, loosen with any unused measured water if needed and divide among 4 bowls.