The laws governing the legal use, storage and carrying of firearms are constantly changing. Below are the applicable laws in the State of  as of 4/10/2013. The below information is designed to be a guide and not the final word. If you have specific questions, please refer to the State of Hawaii legislation at capitol.hawaii.gov. Another great resource is the Honolulu Police Department.

§134-9  Licenses to carry
In an exceptional case, when an applicant shows reason to fear injury to the applicant's person or property, the chief of police of the appropriate county may grant a license to an applicant who is a citizen of the United States of the age of twenty-one years or more or to a duly accredited official representative of a foreign nation of the age of twenty-one years or more to carry a pistol or revolver and ammunition therefore concealed on the person within the county where the license is granted.  Where the urgency or the need has been sufficiently indicated, the respective chief of police may grant to an applicant of good moral character who is a citizen of the United States of the age of twenty-one years or more, is engaged in the protection of life and property, and is not prohibited under section 134-7 from the ownership or possession of a firearm, a license to carry a pistol or revolver and ammunition therefor unconcealed on the person within the county where the license
is granted.  The chief of police of the appropriate county, or the chief's designated representative, shall perform an inquiry on an applicant by using the National Instant Criminal Background Check System, to include a check of the Immigration and Customs Enforcement databases where the applicant is not a citizen of the United States, before any determination to grant a license is made.  Unless renewed, the license shall expire one year from the date of issue.
 
NOTE: Although the law reads that a citizen of the United States, that resides outside of Hawaii can apply for a license, the reality of being issued a Non-Resident Concealed Carry License in the State of Hawaii is not likely.  Hawaii is a "May Issue" state, meaning the decision to issue is left up to the Cheif of Police of the issuing department.  The greater majority of Hawaiian residents that have applied for a carry license have been denied.   It is our understanding that Hawaii has only issued Carry Licenses to employees of private security firms in the past.