Step 1Heat the oven to 350 degrees. On top of the stove, heat a heavy roasting or braising pan over medium-high heat. Add the oil and chicken bones and cook, stirring, just until browned, 3 to 4 minutes. Put the pan in the oven and roast 15 minutes, stirring halfway through the cooking time.
Step 2Add the carrot, onion and garlic to the pan and roast until the vegetables and bones are well caramelized, about 15 minutes more.
Step 3Return the pan to the stovetop and, over medium heat, add the thyme and the wine, stirring and scraping the bottom and sides of the pan to release all of the flavorful bits into the liquid. Continue to cook until the wine has almost completely evaporated.
Step 4Add the stock and simmer, stirring occasionally, until it has reduced by about half so that only about 1 cup of liquid remains. Remove from the heat and strain through a strainer lined with a double thickness of slightly dampened cheesecloth, pressing down on the solids to extract all of their flavor. Discard the solids. Skim the fat. Any leftover jus can be frozen for future use.