(CNN) -- As an American socialite and hotel heiress, Paris Hilton has built up a global brand on her sexy image -- and sometimes very few clothes.

But many believe she has gone a step too far in opening a store selling luxury items in the Muslim holy city of Mecca in Saudi Arabia.

Hilton's rise to worldwide fame was boosted in part by a homemade sex movie that went viral online in 2003, days before the debut of her reality TV series "The Simple Life."

This does not sit well with many in Mecca, which attracts three million Muslim pilgrims from around the world every year.

All Muslims who are able are expected to make the pilgrimage to Mecca at least once in their lifetime, and non-Muslims are not allowed to enter the city. Most Saudi women cover themselves fully with a black abaya.

Hilton introduced her store on the social media site Twitter, when she wrote, "Loving my beautiful new store that just opened at Mecca Mall in Saudi Arabia!" accompanying the post with a picture.