Yes, hot chocolate contains caffeine, though not as much as coffee. A 16-ounce serving of Starbucks hot chocolate, for example, contains 25 milligrams of caffeine. In comparison, a 16-ounce cup of iced coffee from Starbucks contains 165 milligrams of caffeine.
Homemade hot chocolate may be lower in caffeine: 1 tablespoon of Hershey's cocoa powder contains 8 milligrams of caffeine, and 8 ounces of Silk chocolate soy milk has only 4 milligrams of caffeine. Using plain milk, cream or soy milk to make the hot chocolate will decrease the amount of caffeine further. Chocolate ice cream typically contains less than 1 milligram of caffeine per 4-ounce serving.