CANBERRA, Australia—Robyn McIntyre, who lives on the outskirts of Australia’s capital, was in her family room a few months ago when she thought she heard a “chain saw gone ballistic.”

It was actually a drone on its way to deliver a burrito or coffee as part of a test from Wing, which like Google is a subsidiary of Alphabet Inc. One recent day, she said delivery drones flew over her house about 10 times in 2½ hours, making it difficult to focus on working or reading the newspaper.

“There’s one!” said Ms. McIntyre, 64 years old, drinking tea in her living room on a recent Saturday morning. “Oh no, it’s a blowfly. See there, it’s gotten into my head. Every time I hear a high-pitched noise, I think it’s a drone.”

Drones could someday revolutionize e-commerce by cutting delivery times, reducing energy use and lowering costs. For now, they are dividing neighbors in the suburban neighborhood of Bonython, where one of the world’s most advanced drone-delivery tests has taken flight.

Tech companies are tinkering with drone deliveries all over the world. Wing is a step ahead of some by routinely bringing everyday items to customers in an entire neighborhood. Residents can use a smartphone app to order food, hardware supplies and over-the-counter medications from half a dozen retailers. Next year, Wing hopes to move the trial to another part of Canberra and plans to begin a similar test in Finland.