SHENZHEN, China—Big U.S. defense companies brought drones to the battlefield. Now a Chinese company is bringing them to the masses.

In just a few years, SZ DJI Technology Co. has become the world’s biggest consumer drone maker by revenue, selling thousands of its 2.8-pound, square-foot devices for about $1,000 each. In the process, it also has become the first Chinese brand to pioneer a major new global consumer-product category.

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