I don't think its possible to reprogram a new key without an original key. You will have to visit an authorized Chevy dealer for this. If it were that easy, anyone could steal the vehicle by just programming a new key.
From the 98 Silverado owners manual: Each remote keyless entry transmitter is coded to prevent another transmitter from unlocking your vehicle. If a transmitter is lost or stolen, a replacement can be purchased through your dealer. Remember to bring any remaining transmitters with you when you go to your dealer. When the dealer matches the replacement transmitter to your vehicle, any remaining transmitters must also be matched. Once your dealer has coded the new transmitter, the lost transmitter will not unlock your vehicle. Each vehicle can have only four transmitters matched to it.
