Preheat your oven to 200°C | 400° F.
Season chicken with salt, pepper and dried thyme.
Heat a large (34 cm or 13-14 inch) cast iron skillet (or heavy based oven-proof pan), over medium-high heat.
When the skillet (or pan) is hot, add the oil. Sear the chicken breasts on each side until olden and crisp (about 4-5 minutes).
Add the garlic to the centre of the pan, and cook while stirring, for one minute until fragrant.
Pour in the lemon juice, and sprinkle over fresh thyme leaves from 2 sprigs. Place another 2 sprigs around the chicken.
Transfer skillet (or pan), to the oven and cook for 25-30 minutes, or until completely cooked through.
Add the asparagus spears to the pan during the last 12 minutes of cook time.
Garnish with lemon slices and leaves from the remaining sprig of thyme.
Serve immediately.