Yes chains are allowed and required at certain times.
Straight from the CDOT site
During an active Traction Law (also known as a Code 15), motorists must have either snow tires, tires with the mud/snow (M+S) designation, or a four-wheel/all-wheel drive vehicle. All tires must have a minimum one-eighth inch tread. You can also install chains or an alternative traction device (like AutoSock) to be in compliance with the law if your tires aren't adequate.
Find out if your tires meet the minimum one-eighth inch tread requirement by taking the Quarter Test.
Passenger Vehicle Chain Law (Code 16)
During severe winter storms, CDOT will implement a Passenger Vehicle Chain Law (also known as a Code 16). This is the final safety measure before the highway is closed.
When the Passenger Vehicle Chain Law is in effect, every vehicle on the roadway must have chains or an alternative traction device (like AutoSock).
Now I have lived here for well over 25 years and I believe the code 16 has only been around a few years but I have yet to hear of it being implemented as they usually close the road by that time. They do use code 15 regularily in bad weather.