The governor of Guam has signed Bill No. B296-32 [pdf] into law. As per Section 2, the police “shall issue a license” to carry a firearm if the applicant meets the requirements, which are fairly lenient. Aside from being legally eligible to own a gun, applicants must show some proof of training, which can be satisfied by a hunter safety course, an NRA course, or a DD214.
So, the requirements are basically the same as getting a permit in Florida. Guam falls under the appellate jurisdiction of the 9th Circuit, and they may be feeling the pressure after the Peruta ruling.
Guns Save Lives has more information on this.