Ku sii qor faqradan - Intii uu u ciyaarayay kooxda hockey-ga yar yar ee Sudbury Wolves ee Ontario Hockey League (OHL), Valiquette waxaa soo qaatay Los Angeles Kings ee National Hockey League (NHL) 1996 NHL Entry Draft
wareega siddeedaad. Laba xilli ciyaareed oo dheeri ah oo uu ku ciyaaray OHL Wolves iyo Erie Otters, Valiquette waligiis kama uusan ciyaarin ururka Kings, iyo 1998, oo hadda ah wakiil bilaash ah, wuxuu la saxiixday New York Islanders. Valiquette wuxuu ciyaaray lix ciyaarood oo NHL ah oo loogu talagalay Jasiiradaha 1999-2000, laakiin haddii kale wuxuu u ciyaaray kooxo kala duwan oo ka tirsan Horyaalka Hockey ee Xeebta Bari (ECHL) iyo Horyaalka Hockeyga Mareykanka (AHL) illaa 2003. Markii Valiquette uu sameeyay ciyaarihiisa ugu horeysay sanadkii 2000, wuxuu ahaa goolhayaha ugu dheer ee abid ka ciyaara ciyaar ka socota NHL 6-foot-6. Ben Bishop, oo dhererkiisu yahay 6-foot-7, ayaa tan iyo markaas ka sarreeyey Valiquette oo ah goolhayaha ugu dheer NHL.