Pat the chicken thighs dry with paper towels and season both sides with salt and freshly ground black pepper.
Heat 2 tablespoons vegetable oil in a large nonstick skillet over medium-high heat until shimmering.
Add the chicken thighs, smooth side down, in a single layer (cook in batches if the pan is overcrowded). Cook 4–5 minutes, until lightly browned on the first side. Flip and cook 3–4 minutes more, until the second side is browned. Transfer the chicken to a plate and set aside.
Reduce heat to medium. Add the chopped onion and minced garlic to the skillet and sauté 2–3 minutes, stirring and scraping up any browned bits from the bottom of the pan, until the onion is fragrant and starting to soften.
Add 1 teaspoon paprika, 1/2 teaspoon kosher salt, 1/2 teaspoon ground cumin, 1/2 teaspoon ground ginger, 1/4 teaspoon ground cinnamon, 1/4 teaspoon ground turmeric, and 1/4 teaspoon crushed saffron. Stir to coat the onions and garlic with the spices and cook about 30–45 seconds until fragrant.
Add 2/3 cup orzo and stir 30–60 seconds to coat the orzo with the spiced onion mixture.
Pour in 1 1/3 cups chicken stock and bring the mixture to a gentle simmer, scraping the bottom of the pan to deglaze and lift any remaining brown bits.
Nestle the browned chicken thighs back into the skillet in a single layer, pressing them into the orzo so they sit partially in the liquid. Reduce heat to medium-low.
Continue to simmer, stirring occasionally so the orzo does not stick to the bottom, about 8–10 minutes, until the orzo is al dente and a thermometer inserted into the thickest part of the largest thigh registers 165°F.
Stir in 1 tablespoon lemon juice, 1 teaspoon finely grated lemon zest, and 1/2 cup sliced mixed pitted olives. Remove the skillet from the heat.
Spoon the chicken and orzo onto plates or a serving platter and sprinkle with 1/4 cup chopped fresh parsley. Serve warm.