Its about a 12-13 hour drive (give or take for stops) through Utah...once you get past the mountains in CO you should be ok.Edit: Sorry I didn t check back sooner! The chain laws you hear about are for the semi trucks. They are not required for cars. As long as you take your time and have good tires you should be fine. If you are really worried about it you can go through New Mexico but remember that southern colorado often has nasty roads as well, I know the New Mexico mountains can get just as bad as the rocky s do.
I-70 to I-17 (Utah) its safe and takes about 12 hrs. 822 miles.good luck