Season the chicken with salt and pepper on both sides. Heat a large nonstick skillet with 2 tablespoon extra-virgin olive oil, 2 turns of the pan, over medium-high heat. When oil ripples, add chicken and cook 3 minutes on each side then remove and let meat rest and cool.
To the same skillet, add another tablespoon extra-virgin olive oil, 1 turn of the pan, and the butter. Melt butter into extra-virgin olive oil and add the shallots, garlic and capers. Saute 5 minutes then add white wine and reduce 30 seconds. Next, add the juice of 1 lemon and immediately add the spinach - mound up the pan. You will not be able to fit it all in there. Keep turning the spinach and wilting it down until you get it all in there then turn the heat off. Keep some leaves still a bit crisp to vary textures in your salad. Season the spinach with salt and pepper. Chop chicken into little bits and add to the warm salad. Toss to distribute and serve.