Paige Madden, the 23-year-old Olympic swimmer from Alabama, broke the 400-meter freestyle record of the Pan American Games to win the gold medal on Saturday and boost the United States to the top of the medal chart in Chile on the first day of competition. Near the end of the day, the U.S. had nine gold medals out of the 20 medals its athletes had won. Mexico had five gold medals, with Brazil and Canada next with four each.