Such is the case with many new technologies, Mr. Levin said. No one is going to design products that can run only on a one-gigabit-per-second network if no such networks exist, he said. But put a few in place, he added, and soon the supply of applications will drive a growing demand for the faster connections.

Chattanooga’s path to Gig City is part of a transformation that began long before most Americans knew the Internet existed. Named America’s most-polluted city in 1969 because of largely unregulated base of heavy manufacturing, Chattanooga has in the last two decades cleaned its air, rebuilt its waterfront, added an aquarium and become a hub for the arts in eastern Tennessee. In more recent years, an aggressive high-tech economic development plan and an upgrade of the power grid by EPB moved Chattanooga toward the one-gigabit connection.

In 2009, a $111 million federal stimulus grant offered the opportunity to expedite construction of a long-planned fiber-optic network, said David Wade, chief operating officer for the power company. (EPB also had to borrow $219 million of the network’s $330 million cost.) Mr. Wade said it quickly became apparent that customers would be willing to pay for the one-gigabit connection offered over the network.

Chattanooga has been joined in recent years by a handful of other American cities that have experimented with municipally owned fiber-optic networks that offer the fastest Internet connections. Lafayette, La., and Bristol, Va., have also built gigabit networks. Google is building privately owned fiber systems in Kansas City, Kan.; Kansas City, Mo.; and Austin, Tex., and it recently bought a dormant fiber network in Provo, Utah.

The systems are the leading edge of a push for ever-faster Internet and telecommunications infrastructure in a country that badly lags much of the world in the speed and costs of Web connections. Telecommunications specialists say that if the United States does not keep its networks advancing with those in the rest of the world, innovation, business, education and a host of other pursuits could suffer.

Even so, few people, including many who support the systems, argue that everyone in the country now needs a one-gigabit home connection. Much of the public seems to agree. According to Federal Communications Commission statistics, of the households where service of at least 100 megabits per second was available (one-tenth as fast as a gigabit), only 0.12 percent subscribed at the end of 2012. In Chattanooga, one-third of the households and businesses that get electric power from EPB also subscribe to Internet service of at least 100 megabits.

But just as few people a decade ago thought there would be any need for one terabyte of data storage on a desktop computer (more than 200 million pages of text, or more than 200 movies), even the most prescient technology gurus have often underestimated the hunger for computer speed and memory.