Cut tenderloin crosswise into 1/2-inch-thick slices; place between 2 sheets of plastic wrap, and pound to 1/4-inch thickness using a meat mallet or small heavy skillet. Sprinkle pork with salt and pepper. Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add half of pork, and cook 2 minutes on each side or until golden brown. Remove from pan, and repeat procedure with remaining 1 teaspoon oil and pork.
Add shallots to pan, and sauté 1 minute. Remove pan from heat; add chutney, cider, and 1 tablespoon water, scraping pan to loosen browned bits. Return pan to heat, and cook 2 minutes or until sauce is slightly thick. Add pork and accumulated juices to pan. Cook 1 minute or until thoroughly heated. Spoon sauce over pork, and sprinkle with thyme.