It is anticipated that future skies over urban areas will be busy with drones flying back and forth delivering packages. Taking New York City as an extreme example, it is estimated that by 2026, 2600 delivery drones could simultaneously populate the city's airspace. The drone–drone collision rate of “dumb” drones can be calculated by treating them as a gas of large, randomly moving, spherical molecules, using the kinetic theory of gases. Collisions can be avoided by making each drone “smart,” i.e., by giving each a “sense and avoid” capability for detecting and avoiding a potential collision. For smart drones over New York City, the rate of potential collisions, or encounter rate, extends over a surprisingly large range: from 1 to 170,000 encounters/day, depending on input assumptions. This places stringent constraints on the probability that a smart drone encounter will result in a collision, constraints that must be met by the drone operator. Policy implications are discussed.