Cook bacon over medium-high heat until bacon is well browned. Remove from the pan and drain on a paper towel. Drain all but 3 tablespoons of the bacon fat from the pan.
Add diced ribs of Collard and Chard to bacon grease and cook until crispy and browned in places, about 5 minutes. Remove from pan and drain with bacon.
Add garlic to remaining bacon grease and cook 45 seconds. Deglaze with chicken stock and vinegar. Add sugar and greens and partially cover. Lower heat to medium-low and continue to cook for another 30 minutes, checking in from time to time.
Toss bacon and crispy ribs with greens. Season with salt and pepper, to taste.