Place the olive oil and bacon in a medium skillet over medium heat. Cook, stirring often, until the bacon is golden brown and crispy, about 8 minutes. Using a slotted spoon, remove the bacon to a paper-towel-lined plate. Add the onions to the pan and cook slowly in the bacon fat, stirring often, until deeply caramelized, about 15 minutes. Add the onions to the bowl with the bacon and let cool for about 5 minutes. Stir in the yogurt and chives. Cover and refrigerate for at least 1 hour to let the flavors mingle. Serve with the carrot "chips" or pita chips.