Chop the chard stems into 1/2-inch pieces. Stack the chard leaves, roll them tightly into a cylinder, and chop into 1/2-inch strips; chop the strips into halves.
Heat about half the olive oil in a large non-stick skillet over medium heat. Cook chopped chard stems in hot oil until hot, about 1 minute. Stir the chard leaves with the stems; cook and stir together 1 minutes more.
Drizzle remaining olive oil over the mixture and stir to coat. Continue cooking and stirring until the leaves are nearly wilted, 4 to 5 minutes.
Remove from heat and immediately sprinkle kosher salt and squeeze lime half over the chard. Stir to season evenly.
