Drone delivery services are becoming increasingly available, but they introduce new consumer privacy risks. As a result of safety regulations that require drones to broadcast their locations, third-party observers may link customers to their purchases by following a delivery from vendor to customer. These privacy risks can be reduced with routing strategies that aggregate customer orders, at the potential cost of additional delivery wait times or fees. This study measures the importance of these privacy risks to delivery service customers, their willingness to pay for privacy, and how this differs across consumer groups and product types. We developed a discrete choice experiment and mode choice logit models using data from over 3700 U.S. consumers who chose between ground vehicle versus drone delivery across a range of privacy, delivery fee, and wait time options. Preferences were tested for various product types: take-out food, liquor store items, groceries, and prescription medications. Results show offering privacy enhancements significantly increased consumers’ likelihood of choosing drone delivery. Without privacy enhancements, when fees and wait times were the same, consumers chose ground vehicle 4 times more often than drone. Offering privacy for the drone option closed this gap. Yet preferences differ by demographic group. Males and frequent e-commerce users were more likely to prefer drone regardless of privacy, while privacy improvements had a significantly larger impact on females and younger consumers. We measured consumers’ value of privacy in both money and time. The value of privacy for medications delivery was about twice that for other product types. The value of privacy was then highest for liquor store items, then groceries, then take-out food. Our results can inform delivery service planning as well as contribute to a broader understanding of how consumers value privacy and methods to measure that valuation.