Kammala jumla mai zuwa: Yayin wasa hockey na matasa don Sudbury Wolves na Ontario Hockey League (OHL), Los Angeles Kings na National Hockey League (NHL) sun tsara Valiquette a cikin
1996 NHL Entry Draft a zagaye na takwas. Yin wasa na karin yanayi biyu a cikin OHL tare da Wolves da Erie Otters, Valiquette bai taɓa yin wasa da ƙungiyar Kings ba, kuma a cikin 1998, yanzu dan wasa ne mai 'yanci, ya sanya hannu tare da New York Islanders. Valiquette ya taka leda a wasanni shida na NHL don tsibirin Islanders a 1999-2000, amma in ba haka ba ya taka leda a kungiyoyi daban-daban a gasar East Coast Hockey League (ECHL) da American Hockey League (AHL) har zuwa 2003. Lokacin da Valiquette ya fara wasa a 2000, shi ne mafi tsayi mai tsaron gida da ya taba buga wasa a NHL a 6-foot-6. Ben Bishop, yana tsaye 6-foot-7, tun daga lokacin ya wuce Valiquette a matsayin mafi tsayi mai tsaron gidan NHL.