For the basil chimichurri:
In a small bowl, mix all the ingredients to combine well. Set aside.
For the chicken:
Heat the olive oil in a large cast-iron skillet set over medium-high heat.
Season the chicken with the salt and pepper on both sides and place the chicken pieces skin-side down in the skillet. Fill in the pan with the potatoes. You want the pan really full so that the surface area is completely covered with chicken and potatoes.
Cover with a lid and cook for 8 to 10 minutes, until the chicken has released its juices and everything is golden.
Flip the chicken, cover again, and cook for another 10 minutes, or until the thickest part of the chicken reaches 165 F.
Remove from heat, add dollops of chimichurri on top and serve immediately.