Preheat the oven to 450 degrees F and line a baking sheet with foil. Loosen the chicken skin with your fingers; rub 1 tablespoon olive oil over and under the skin. Stuff the lemon slices and garlic under the skin; season the outside with salt and pepper. Transfer the chicken to the prepared baking sheet, skin-side up. Roast until crisp and cooked through, about 25 minutes. Let rest 5 minutes.
Meanwhile, heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the asparagus and cook, stirring occasionally, until tender and browned in spots, 2 to 3 minutes. Transfer to a plate.
Reduce the heat to medium and add the remaining 1 tablespoon olive oil, the onion and thyme to the skillet; cook, stirring, until the onion is tender, about 3 minutes. Stir in the orzo and cook, stirring, until lightly toasted, 2 to 3 minutes. Add 2 1/2 cups water and a pinch of salt. Simmer, stirring occasionally, until the orzo is tender, about 15 minutes. Remove from the heat; discard the thyme and stir in the asparagus and chives. Season with salt and pepper. Serve with the chicken and lemon wedges.