Heat oil in a 12-inch heavy skillet over medium heat until it shimmers, then cook garlic, stirring, until golden, about 3 minutes. Transfer garlic with a slotted spoon to paper towels to drain.
Cook onion in oil remaining in skillet over medium heat, stirring occasionally, until softened, 3 to 5 minutes. Add currants and cook, stirring, until plumped, about 1 minute.
Stir chard stems into onion mixture with water and 3/4 teaspoon each of salt and pepper. Cook, covered, over medium-high heat until almost tender, about 5 minutes. Stir in chard leaves and cook, covered, until stems and leaves are tender, about 5 minutes.
Meanwhile, cook spaghetti in a pasta pot of boiling salted water (2 tablespoons salt for 5 quarts water) until al dente. Reserve 1 cup pasta-cooking water and drain spaghetti.
Toss spaghetti with chard, olives, and 1/2 cup cooking water, adding more cooking water if necessary. Season with salt and pepper. Serve sprinkled with feta and garlic chips.