(FORTUNE Magazine) – UCLA professor James Heath is trying to build a computer--though you wouldn't know it from the lab where he works. There's hardly a sliver of silicon to be found. No one wears a bunny suit. In one of the rooms, a run-of-the-mill organic chemistry lab, a postdoc named Julie hovers over a workspace strewn with test tubes, flasks, various bottles of chemicals. "There's usually a lot of shit lying around in here," she says apologetically as she picks up one of the flasks. It's coated with a yellowish-orange powder. "This has been sitting here a couple of weeks." She hands the flask to Heath.

"That's the stuff!" he says happily. Unimpressive as it seems, the yellow crust on the flask is computer hardware: a billion trillion switches, each composed of just a single molecule. It is the culmination of five years of work, and it could be the key to the computer of the future and the vitality of the $200-billion-a-year semiconductor industry.

Heath's vision is not some quixotic sci-fi dream. Over the next 20 years or so, technologists may well have to invent a new way of making chips if they want to prolong the rapid growth in processing power that has led to the development of personal computers, digital media, and the Internet. For the past 35 years, hardware and software companies could rely on Moore's law, which predicts that chipmakers will be able to double the number of transistors on a silicon chip (and therefore boost the chip's speed and power) every 18 months or so. The problem is, there are only so many transistors you can cram on a solid-state silicon chip; the laws of quantum mechanics dictate that the smaller components get (and the closer they are to one another) the less reliable they become in moving an electronic signal through a machine. Jam-packed chips also become prohibitively expensive to manufacture. Some industry insiders estimate that by 2015 the cost of building a traditional chip fab will reach $100 billion.

So prominent chemists across the country--at Hewlett-Packard, IBM, Yale, Rice, Stanford, and Harvard, as well as at UCLA--are experimenting with a different sort of fabrication. Instead of chiseling chips from blocks of silicon, they are assembling a tinier type of computer component from the building blocks of matter. Their idea: to create new kinds of molecules that behave the way transistors and wires do, and then figure out how to arrange them into workable circuits.

It's a far-out notion--one that requires radically new approaches to manufacturing and software programming--but the scientists are beginning to get somewhere with it. Heath's yellow powder is made up of molecules called rotaxanes, which act as switches just as transistors do. Coming up with molecules that can move predictably from one state ("on") to another ("off") is a huge breakthrough in itself; Heath and his team have also succeeded in attaching their minuscule switches to tiny wires. The new components do not operate as dependably as silicon transistors do, but Heath and his partners at Hewlett-Packard have solved that problem with a redundant wiring technique that routes signals around imperfect molecular switches.

Heath thinks he might be able to build a rudimentary computer within a couple of years. "It won't be a computer you'll be proud of," he says, "but it will work." Then, he believes, if he can scale the whole thing up to a capacity of one megabyte (about the amount of memory in a cell phone), molecular computing becomes, as Heath puts it, "an engineering project"--in other words, a technology that companies can begin to muck around with themselves.

A serious type whose ponytail and Birkenstocks belie his intensity in the lab, Heath, 39, never really intended to get involved in the computer industry. As a graduate student he worked with the team at Rice University that discovered buckminsterfullerene (or "buckyballs"), a new class of all-carbon materials with the potential for countless industrial applications. As a professor he had always wanted to work in nanotechnology, which uses chemistry to build submicroscopic machines. Heath says that he decided to explore molecular computing because he felt it could be a great proving ground. "I thought designing a computer would be a nice driver for the research," he says.

Building a rudimentary molecular computer, as modest as its abilities may be, will entail a long, hard slog. Heath has been able to craft a molecular memory circuit (like those found in a DRAM chip for holding software programs while they're running) but not a logic circuit (like the ones in a Pentium microprocessor). Once he cracks the logic circuit nut, he'll then need to find a dependable way to connect his molecular circuits to one other and to inputs from the outside world, like a keyboard or mouse. That's no mean feat, considering that it involves linking chaotic arrays of molecules and carbon wires that are just atoms wide to metallic wires 50 times their size.

With a Nobel Prize not beyond the realm of possibility for the inventor of the chip of the future, competitive noises sometimes reach a high pitch. Heath, for instance, has discovered a way to build a working circuit, which he says puts him ahead of the pack. But at least two of his rivals claim that their approaches will be better in the long run. Just because molecular transistors are tiny doesn't mean the egos working on them are.

--Eryn Brown