Season chicken with salt and pepper. In a large deep skillet or Dutch oven, heat 1 tbsp (15 mL) oil over medium-high heat. Add chicken and cook, turning once, until golden brown, about 10 min. Transfer chicken to a plate and set aside.
Reduce heat to medium and return pan to heat. Add remaining oil to pan. Add onion, garlic and thyme and cook, stirring often, until softened and aromatic, about 5 min. Sprinkle with flour and cook, stirring, 1 min. Stir in chicken broth, 3/4 cup (175 mL) water, lemon zest, lemon juice and capers and bring to a boil, scraping up any brown bits from bottom of pan. Add potatoes, cover, reduce heat to medium-low and cook, about 10 min.
Add chicken, bone side up, nestled amongst the potatoes. Cover and cook until potatoes are tender, about 20 min. Turn chicken over and lay asparagus over chicken and potatoes. Cover and cook until asparagus is tender, liquid is reduced and juices run clear when chicken is pierced, about 7 min (or when an instant read thermometer inserted into the thickest part of the chicken, away from the bone, reads 165°F / 74°C). Sprinkle with parsley.
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