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In 1939 Colonel Sanders perfected his secret blend of eleven herbs and spices for chicken in his Corbin, Kentucky truck stop. It wasn’t until 1952 when the world first saw “Kentucky Fried Chicken”. The world’s first restaurant featuring Kentucky Fried Chicken was also its first franchise in Utah, Harman Café. The new franchise owner, Pete Harman, decided that the chicken pieces would sell better in Salt Lake City with the more exotic sounding Kentucky Fried Chicken rather than Utah Fried Chicken. This is the story of KFC’s first franchise owner and how he impacted the identity and direction of the chain and the franchise movement.



In 1952
The Colonel begins actively franchising his chicken business by traveling from town to town and cooking batches of chicken for restaurant owners and employees. The Colonel awards Pete Harman of Salt Lake City with the first KFC franchise. A handshake agreement stipulates a payment of a nickel to Sanders for each chicken sold.

So technically SLC is the first place to have a KFC, but not the first place to have a restaurant run by Colonel Sanders.

See the source link for the complete history of KFC  
Sources: http://www.kfc.com/about/history.asp