A 6'0" defenceman, Delmore played junior hockey for the North Bay Centennials and later for the Sarnia Sting of the Ontario Hockey League (OHL). He went undrafted in 1997 and signed as a free agent with the Philadelphia Flyers, making his NHL debut during the 1998–99 season. Delmore was the first rookie defenceman to record a hat-trick in the playoffs. He also scored the overtime winner in Game 3 of the 2000 Eastern Conference Semifinals as Philadelphia defeated the Pittsburgh Penguins, 4–3. While playing for the Nashville Predators during the 2002–03 NHL season, he tied Sergei Gonchar and Nicklas Lidström for most goals (18) by a defenseman.