Bring the chicken stock and water to a simmer in a saucepan; keep warm over low heat. Melt the butter in a medium nonstick saucepan. Add the orzo to the butter and cook over moderately high heat, stirring often, until the orzo is golden, about 8 minutes. Add 1 cup of the hot stock mixture and cook, stirring gently, until all of the stock is absorbed. Gradually add more of the stock mixture, 1 cup at a time, and cook, stirring frequently, until the orzo is al dente and creamy but not soupy, about 20 minutes.
Meanwhile, heat the olive oil in a large nonstick skillet. Add the shallot and Swiss chard stems and cook over moderately high heat, stirring occasionally, until the stems are tender and lightly browned, about 7 minutes. Add the chard leaves and cook over moderately high heat, tossing, until the leaves are wilted, about 2 minutes. Add the vinegar. Stir the chard and the Fontina and Parmesan cheeses into the risotto, season with salt and pepper and serve.
Wine Recommendation: Savory Swiss chard and nutty Fontina will pair successfully with a crisp, lean Soave from Italy, such as the 1998 Bolla Tufaie Castellaro or the 1998 Anselmi San Vincenzo.