ON A WARM AFTERNOON in late October 2005, El Capitan towers 3,600 feet above Yosemite Valley, gray and massive like a battleship propped on one end. Tiny yellow portaledges and speck-size climbers dangle off the granite face on invisible ropes. From this distance, the climbers appear motionless, all their toil swallowed up by the enormous scale.

Twenty-five hundred feet up, on the toughest move on one of El Cap's toughest routes, Steph Davis is scraping at the rock with half-frozen feet when her right climbing shoe slips, and just like that she's falling 30 feet through the air. Her rope snaps taut and she jerks to a stop, swinging in space. She yells down to her belayer—a 38-year-old woman named Cybele Blood, whom Davis recruited from Yosemite's dirtbag contingent—to let her know she's not hurt. She's just annoyed.

"Great," she mutters, knowing there's only one thing to do: suck it up and keep climbing.

Davis is eight days into her attempt to become the first woman to free-climb the Salathé Wall, a 35-pitch route on El Cap's prominent southwest face, and by her estimate she should be done already. But from the beginning, nothing's gone according to plan.

For starters, there's the weather. By turns blazingly hot, then sleety, windy, and cold, these are the kinds of erratic conditions that can turn ugly fast—as they did almost exactly a year ago, when a snowstorm hit El Cap, trapping two Japanese climbers who froze to death before rescuers could reach them. Davis isn't equipped for that kind of weather. She's wearing light rock shoes, climbing tights, long underwear, and a gauzy wind jacket. Her only other gear: a summer-weight sleeping bag, a tiny portable espresso maker, and not nearly enough food.

But her main problem is doubt, an awful, lurking worry that she's simply outmatched by the Salathé's hardest pitch, 150 feet of flinty holds known as the Enduro Headwall. And that's a bad sign, because Davis's greatest assets aren't natural athletic talent and flawless technique but sheer will and a brainy, methodical work ethic. The 33-year-old trained alone all summer for this climb, rappelling hundreds of feet off El Cap to practice the Salathé's hardest sections over and over. But leading a 5.13 climb—which is like spidering up the side of a skyscraper, clinging to crimps no bigger than a lentil—is a different story altogether, and Davis is falling. A lot.

Unlike traditional aid climbing, where it's OK to hang off ropes while you scale a wall, free climbing requires that you use only your hands and feet to climb the rock's natural cracks and flakes. Protective devices are there to catch you if you fall, as is your belayer. And while falling isn't forbidden, it's definitely inconvenient. Take a whipper off the wall and you have to lower yourself to the start of the pitch and climb it again, cleanly.

Davis has been stuck on this one section all day. Now, with daylight fading, she's doomed to spend the night on a granite ledge barely wider than a diving board, 2,500 feet of vertical drop yawning beneath her. A thought crosses her mind: Why not just quit and go down?

The truth is, whether she succeeds or fails on the Salathé, not many people will know or care. Free climbing is a niche pursuit that most of the world doesn't even understand. Davis is a sponsored professional—she makes a decent living through endorsements from Patagonia, Five Ten, Clif Bar, and Black Diamond—so she needs to keep performing at a top level. But she'll never get rich or famous doing this.

"Let's just say," she laughs, "that it's not as lucrative as golf!"

In fact, the only people likely to notice are other climbers, which can be a mixed bag. Climbing is a small and sometimes snarky community, where everybody has opinions about everybody else. Davis earns plenty of praise—"She's a superstar," says alpine climber Mark Synnott—but because she's sponsored, she hears plenty of secondhand griping that she's sold out.

This may seem like skimpy payoff for someone who's worked tirelessly for the past 15 years to become one of the best women climbers in the world. And make no mistake: Davis, along with climbers like 26-year-old Beth Rodden and 45-year-old legend Lynn Hill, is among the all-time elite. She's put up first ascents on hellish alpine faces from Pakistan to Patagonia, freezing for days at a time in snow caves, nearly getting clobbered by falling chunks of ice, and rappelling solo down thousand-foot faces while her husband, 34-year-old pro climber Dean Potter, BASE-jumps off the top.

All this from a woman who grew up playing piano, not sports, never heard of climbing until the relatively ancient age of 18, but somehow had the nerve to quit law school to follow her dream, despite the fact that her parents routinely told her she was nuts. In the risk-versus-rewards department, do the rewards even come close?