To make chimichurri, stir all ingredients together in a small bowl. Allow to sit for 5-10 minutes to release all of the flavours. (Alternatively, you can whiz everything together in a blender or food processor.) Chimichurri can be prepped up to 24 hours ahead, if you like; store in the fridge.
To start the skillet, spoon 1/4 cup chimichurri out into a shallow dish, reserving the rest to serve later. Nestle the chicken in the dish to coat, and let marinate at room temperature for about 15 minutes.
While the chicken marinates, warm oil in a large cast-iron skillet over medium-high heat. When hot, add the asparagus and season it with a bit of salt and pepper. Cook for 3-4 minutes, tossing occasionally, just until crisp-tender and slightly charred. Remove asparagus to a plate and set aside.
Add the marinated chicken to the skillet. Cook pieces for 3-4 minutes on each side, until the outside is golden and the inside is cooked through. Return asparagus to the skillet, spoon a little chimichurri over everything, and serve with additional chimichurri at the table. Enjoy!