Unfortunately, it appears to be real. Here is a link to the instructions from the Delaware Superior Court on how to obtain a license. Number 1 covered in the instructions is the aforementioned publishing of your application in the paper. Note that it also requires references from 5 people in your county farther down.
The application itself also requests your specific reason for wanting a concealed carry permit (protection of property or self, etc).
Instructions:
http://courts.delaware.gov/forms/download.aspx?ID=33278
Application:
http://courts.delaware.gov/forms/download.aspx?ID=33068
Sad really...