The riddle
What Can You Break Without Touching It?
Breaking something that has no parts
Nothing about a promise can snap, so "break" has to mean something else. Merriam-Webster includes the sense of failing to keep an agreement or a vow, and a promise is the standard example. The word promise comes from a Latin verb meaning to send forth, which fits, since a promise sends words out ahead of the action. Keeping it and breaking it are the two ways it can end, and the verbs pair naturally in everyday speech. Because a promise is spoken, it can be broken from across a room or from another town.
Silence as another answer
Silence is the other answer that turns up, and it fits the wording: speaking breaks a silence without anyone laying a hand on it. A 1903 collection by Dean Rivers, titled Conundrums, Riddles and Puzzles, has a riddle of a similar kind, asking what is broken just by naming it, and its answer is silence. Promise remains the more common answer to this exact question.
A physical trap in the question
Most people picture something fragile, such as a plate or an egg, because "break" suggests hands. The words "without touching" are meant to push attention toward something abstract. A listener who gives a physical answer has to explain how the object could break from a distance, and that is usually the moment the group sees the trick.
Using it with a group
Ask for a show of hands before revealing the answer. Many guesses will be physical, and the contrast with the real answer is the point. A follow-up question that works well is "what else can be kept or broken?", which leads straight back to the promise.