Heat the olive oil in skillet over medium-high heat.
Cook the chicken 6-7 minutes per side until internal temperature reaches 165 F.
Rest 10 minutes, then slice thinly against the grain.
Preheat oven to the highest setting, preferably 500 F and preheat a pizza stone or steel inside for 45 minutes.
To make the pesto, pulse 3 cups of arugula, pistachios, garlic, and cheese in a food processor until coarsely chopped.
Add the lemon juice, then drizzle in the olive oil while processing. Season with salt, and set aside.
On a lightly floured surface, stretch the dough to a 12-inch circle.
Transfer to the preheated pizza stone.
Spread the pesto over the dough, leaving a ½-inch border.
Distribute the sliced chicken and dot with ricotta in spoonfuls.
Transfer the pizza to the oven and bake for 10-12 minutes until the crust is browned and blistered.
Top with the remaining fresh arugula, and place the whole burrata ball in the center of the pizza. Top with lemon zest, a drizzle of olive oil, and flaky salt. Serve immediately.