Aebischer was drafted 161st overall by the Colorado Avalanche in the 1997 NHL Entry Draft. He moved to North America in 1997 and spent the 1997–98 season in the ECHL, first with the Chesapeake Icebreakers and then with the Wheeling Nailers. He spent the next two seasons with Colorado's American Hockey League (AHL) affiliate, the Hershey Bears, with whom he compiled a 46-33-7 record. When the Avalanche traded backup goaltender Marc Denis to the Columbus Blue Jackets in the summer of 2000, Aebischer became the full-time backup to starting goaltender Patrick Roy.