1. Bring a large pot of salted water to a boil.
2. Heat a large skillet over medium-high heat, and swirl in the oil. Add the artichokes to the pan, and sear well on one side for 3 minutes. Sprinkle shallots and garlic around the artichokes, stirring everything around in the pan to brown evenly. Add Swiss chard, salt, pepper, lemon zest, and chicken broth, and bring to a boil, scraping the bottom of the pan. Lower heat to medium, cover, and cook for 10 more minutes.
3. Cook pasta according to package directions, then drain and return to the pot with the artichoke mixture. Divide among 4 bowls, and top with crumbled goat cheese.