From the Lower 48 or Canada:
Take the Klondike Loop from Whitehorse to Dawson City. Then travel the Top of the World Highway from Dawson City. This will turn into the Taylor Highway at the cutoff to Eagle. Just after you cross Chicken Creek, turn left toward downtown Chicken (which you can't see from the highway.) You will travel 1/8th of a mile and then you can't miss it!
From the Rest of Alaska:
Take the Alaska Highway. 12 miles west of Tok, turn onto the Taylor Highway cutoff. Chicken is approximately 68 miles from this junction. Take the first exit to the right. You can't see Chicken from the road, but it's just 1/8th of a mile off the highway. If you cross Chicken Creek, you've gone too far.
A "Milepost" travel book is highly recommended for any travel through Alaska.