Varvara Lepchenko Continues Surprising Run to French Open's Round of 16 Varvara Lepchenko is one of two Americans to reach the fourth round at Roland Garros. She defeated Francesca Schiavone, the 2010 French Open winner. PARIS - The longer Varvara Lepchenko held on against Francesca Schiavone, the more Lepchenko implored herself to fight. That last word is something of a mantra for Lepchenko, a tidy way to explain an untidy narrative, the simplest way to summarize her life. Fight Lepchenko did against Schiavone, the Italian who won the French Open in 2010 and dropped to kiss the clay. Schiavone had struggled this season and entered this tournament seeded 14th, but that hardly made her any less dangerous at Roland Garros. As Lepchenko fell behind and went ahead and fell behind and went ahead, she said her thoughts alternated between "this is going to be over soon" and "you can do it." Ultimately, Lepchenko prevailed, 3-6, 6-3, 8-6, on Saturday to move into the fourth round of the French Open. She had never advanced beyond the second round of any previous Grand Slam tournament. So it continued, this strange tournament for American women, where up is down and right is left, where Serena Williams lost in the first round of a Grand Slam for the first time in her career and the two Americans who remain among the final 16 are named Lepchenko and Stephens, as in Sloane. This was only the second time since the major tournaments increased the number of seeded players to 32 (2001, Wimbledon) that two unseeded Americans advanced to the second week. "I mean, I didn't even expect it," Lepchenko said. Lepchenko, now 26, spent most of her childhood in Uzbekistan, where her parents studied in college. Her mother, Larisa, earned a degree in math, her father, Peter, became an engineer.) But money was tight and opportunity was scarce and when Peter Lepchenko took his daughters to Florida in 2002, they never returned home. Eventually, the family was granted political asylum. But Lepchenko did not see her mother for five years. Lepchenko became an American citizen on Sept. At 18, Lepchenko went to Allentown, Pa., where her host was Shari Butz McKeever, who allowed the family to live in her house, rent free. The Lepchenkos could not afford an apartment then, but moved out when they could and remained in Allentown. Before Lepchenko won three matches at the 2012 French Open, she won consecutive titles at the Westend Racquet Club in South Whitehall Township, Pa., in 2005 and 2006. That became her initial training ground. An inauspicious start indeed. Last year, Lepchenko said she increased her training, under the guidance of coaches from the United States Tennis Association. She worked so hard, she said, "I was dying." Those coaches told her she could reach the top 50. When she returned from the Australian Open, one coach, the program's general manager, Patrick McEnroe, told Lepchenko, "We need more women in the second week." Here they are, with two unexpected, unranked charges into Week 2. Stephens dispatched Mathilde Johansson easily on Friday, and Lepchenko followed on Saturday. This further complicated the competition for Olympic slots at this summer's London Games. Players must be ranked no lower than 56th and no more than four from the same country can qualify. Although it looked early in this tournament as if Venus Williams had secured her slot, the continued success of Lepchenko and Stephens called that into question. Then there was Christina McHale, currently ranked 36th, the second-highest among American women. She threw a scare into Li Na, the defending champion, in a 3-6, 6-2, 6-1 defeat on Saturday. For much of their respective matches, McHale and Lepchenko were on at the same time, and when McHale shot to her first-set lead, it appeared two young Americans could upset the last two women's singles champions at Roland Garros. "She's a very dangerous player," Li said of McHale. The same could be said of this group of young Americans, McHale and Lepchenko and Stephens and Vania King. They started the French Open with a 10-0 record, and had Serena Williams won her first match, the Americans would have placed their most female players in the second round since 2003. Of all those, Lepchenko was perhaps the most surprising. Ten years ago she came to the United States to seek asylum. Ten years later she looks likely to represent the United States in the Olympics, a narrative, for the fighter, that sounds an awful lot like the American dream.