Kjeldbjerg started playing football lower-league clubs
Holstebro Boldklub and
Viborg FF, before moving to Danish top-flight team
Silkeborg IF. In August 1993, he moved abroad in
England. He was bought by
Chelsea in the
FA Premier League, in a
transfer deal worth £485,000. Eighty years after
Nils Middelboe made his Chelsea debut in 1993, Kjeldbjerg became the second Dane to play for the club. He stayed with Chelsea for four years. In a game against
Millwall in February 1995, Kjeldbjerg dislocated his shoulder, the first incident in a long list of injuries. He injured a
ligament in his left knee, and was unable to fully recover. He ended his professional football career in 1997, only 28 years old. ==International career==