* Automatic Transmission: A 2001 Chevy 1500 4x4 with an automatic transmission should generally be towed on a flatbed tow truck. Towing it on a dolly or behind another vehicle with the drive wheels on the ground can damage the transmission.
* Manual Transmission: A 2001 Chevy 1500 4x4 with a manual transmission can often be towed with the drive wheels off the ground (using a dolly) *provided the wheels are not locked*. However, always consult your owner's manual for the manufacturer's specific recommendations. A flatbed is still the safest option.
In short: While it's *possible* to tow it other ways depending on the transmission, using a flatbed tow truck is always the safest and recommended method to avoid potential damage. This is particularly crucial for automatic transmissions. Always check your owner's manual for specific towing instructions from the manufacturer.
