A woman with rather large cleavage was told not to board a 6am Southwest Airlines flight from Las Vegas to New York.  The woman was actually wearing a cotton dress, loosely open flannel shirt, and scarf. But because she was showing too much cleavage, airline officials deemed it in appropriate and asked her to cover up or not board the plane.  

According to a story from CBS New York , the woman did not cover up and boarded the plane anyway.

I didn't want to let the representative's Big Feelings about my breasts change the way I intended to board my flight, and lo and behold, the plane didn't fall out of the sky...my cleavage did not interfere with the plane's ability to function properly. Imagine that!
Southwest Airline Passenger

Southwest Airlines has since offered the passenger an apology and a refund as a gesture of goodwill.   The passenger said she chose Southwest because they were the cheapest and will not fly Southwest again.   She also said she was not trying to set a fashion statement but only wanted to be comfortable as Las Vegas was 105 degrees.

A Southwest spokesperson also said the airline was in their right and their Contract of Carriage allows them to refuse to transport a customer whose clothing is lewd, obscene, or patently offensive.