Hillman won three gold medals at the 1904 Olympics in St. Louis, Missouri, taking the flat 400 metres, the 200 metres hurdles and the 400 metres hurdles. He had Olympic record times in all three events, but Hillman tripped one hurdle in the 400 metres, which meant that his time of 53.0 seconds could not be counted as a world record (the record had stood at 57.2 seconds since 1891). In addition, the race was run over hurdles that were too low at 76 centimetres instead of the normal 91,4.
En route to Greece for the 1906 Summer Olympics, Hillman was one of a half-dozen athletes who were injured by an enormous wave that washed over the deck of the ship. He finished fifth in the 400 metres, his only event that year.
Hillman won a silver medal in the 400 metres hurdles at the 1908 Summer Olympics, setting a short-lived record in the second round. He and Charles Bacon of the USA went over the last hurdle simultaneously, but Bacon won the run to the tape to win in a world record 55.0 seconds. Hillman's time in the race was 55.3 seconds.
The track coach at Dartmouth College from 1910 until his death, Hillman advised hurdlers to swallow raw eggs, which he believed to be "excellent for the wind and stomach." He was on the Olympic track and field coaching staff in 1924, 1928, and 1932 Summer Olympics. One of his most famous athletes was Canadian hurdler Earl Thomson, the winner of the gold medal in the 110 metres hurdles at the 1920 Summer Olympics.