Season the chicken breasts with salt and pepper. In a large skillet, heat the olive oil over medium high heat. Add the chicken breasts and sauté until done, about 4 to 5 minute on each side. Remove the chicken breasts to a plate and set aside. Do not wipe out the skillet!
Add the shallot to the skillet and sauté over medium high heat for 3 to 4 minutes until tender. Add the white wine and stir to scrape up all the little flavorful bits that may be stuck to the bottom of the skillet. Simmer for about 2 minutes until the wine reduces by half. Add in the broth, and return to a simmer, stirring occasionally for another 4 minutes until the mixture reduces slightly. Add the mustard, arugula, cream and butter, and stir until the butter is melted and arugula is wilted.