Klochkova was born into an athletic family (both parents competed in track and field) and took up swimming at age seven. She began competing internationally in her mid-teens and took silver in the 400-metre individual medley at the world championships in early 1998. At the European championships the following year, she won both individual medleys in addition to placing third in the 400-metre freestyle event. At the 2000 Olympic Games in Sydney, Australia, she broke a world record in the 400-metre medley (4 min 33.59 sec). She followed up with an Olympic record in the 200-metre medley (2 min 10.68 sec) and concluded with a silver medal in the 800-metre freestyle (8 min 22.66 sec). Klochkova's gold medals at the 2004 Olympic Games in Athens in the 200 metre (2 min 11.14 sec) and the 400 metre (4 min 34.83 sec) matched her performance at the previous Olympics.