In a very large skillet heat 1 tablespoon olive oil over medium heat. Add the onions and cook stirring frequently until soft and caramelized, about 20 minutes. Transfer the onions to a bowl and set aside.
Pat the chop dry with paper towels and rub with salt and pepper both sides.
Return the skillet to the heat and add the remaining 2 tablespoons olive oil over medium-high. Add all the pork chops, making sure that they are not crowded in the skillet, you may have to cook the chops in 2 batches. Cook the chops until well-browned on one side, around 5 minutes, make sure that they do not burn. Turn and cook the other side until the chops are done. If they start to burn, lower the heat to medium. Remove from the heat and place in a dish, cover with aluminum foil and let them rest.
Meanwhile, put the skillet back to medium heat and add the balsamic and scraping the skillet. Add the caramelized onions and simmer gently and the vinegar is reduced to coat the onions. Season with salt and pepper to taste and add the fresh thyme. Serve over the pork chops immediately.