Hold each asparagus spear at both ends and bend until it snaps naturally. Discard the tough ends. Cut the tender tops into 2-inch pieces and set aside. Reserve about 1 cup of the prettiest tips for garnish.

Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Season chicken with salt and pepper, then add to the pot in a single layer. Cook undisturbed for 4-5 minutes until golden brown on one side, then stir and cook 2 minutes more. The chicken does not need to be fully cooked through. Transfer to a plate.

Reduce heat to medium. Add onion to the same pot and cook, scraping up any browned bits, until softened and translucent, about 5 minutes. Add garlic and thyme and cook 1 minute until fragrant.

Add the chicken broth and all but the reserved asparagus tips. Bring to a boil, then reduce heat and simmer for 8-10 minutes until the asparagus is very tender and easily pierced with a knife.

Working in batches if needed, carefully transfer the soup to a blender and puree until completely smooth, or use an immersion blender directly in the pot. Return soup to low heat and stir in the heavy cream.

Add the browned chicken and reserved asparagus tips to the soup. Simmer gently for 5-7 minutes until the chicken is cooked through and the tips are tender-crisp. Stir in lemon juice and taste for seasoning. Ladle into bowls and top with chives and Parmesan.