Bring barley to simmer over medium-high heat and cook, covered, until barley is just cooked through but still somewhat firm in center, 10 to 15 minutes. Stir in squash and chard stems and cook, covered, until vegetables are tender, 10 to 15 minutes. Stir in chard leaves, decrease heat to medium, and cook, uncovered, until leaves are tender and mixture is thickened into risotto-like consistency, 2 to 5 minutes. Off heat, stir in Parmesan and vinegar. Season with salt and pepper to taste.