Preheat the oven to 375 F.
Clean the potatoes then cut into 1/2 inch cubes. Line a rimmed baking sheet with parchment paper, then place the potatoes on the baking sheet and toss with olive oil, 3/4 teaspoon coarse sea salt, and black pepper. Spread the potatoes across the pan and bake for 20 minutes.
While the potatoes are cooking, make the pesto. Place the spinach, walnuts, Parmesan, garlic powder, salt, and pepper in a food processor. Pulse until the mixture has a coarse, sandlike texture. Then, add the lemon juice to food processor, then turn it to high speed and slowly drizzle in the olive oil. Keep the food processor running for an additional minute, until a smooth consistency is achieved.
Coat the chicken with 1/3 cup pesto and 1 teaspoon coarse sea salt.
Remove the potatoes from the oven, then add the chicken to the pan. Bake for 25 minutes, until potatoes are easily pierced with a fork and chicken is fully cooked through. Remove from oven and serve with additional pesto.