オールボーBK
Raised in Thisted, Grønkjær started his career with local team Thisted FC. Earlier in his career he was told that he could have been a sprinter. He moved on to defending Danish Superliga champions Aalborg Boldspilklub (AaB) in 1995. He played almost 100 matches for the club, including games in the European 1995–96 UEFA Champions League tournament. He attracted the attention of a string of European top clubs.