If you've got a cloud storage account (like Dropbox, OneDrive, etc.), and are using Windows Vista or newer*, you can move the "Paragon Chat" folder to it, and use the SysInternals "junction" or the Windows 8+ "mklink" command to create a directory junction to the cloud storage folder. That lets you have the same characters across multiple PCs, and gives you the added benefit of backups in case your PC dies.
Example:
These steps only need to be run on the PC you've got your characters on1. Move "Paragon Chat" from the %APPDATA% folder to your cloud storage. Make note of the full path to which you've moved it, e.g. "C:\Users\MyAccount\Dropbox\Paragon Chat".
These steps need to be run on every PC that you want to play Paragon Chat on2. If using Windows Vista or 7,
download the "junction" tool from the Microsoft SysInternals website. Place it in C:\Windows\System32 or another folder. If using Windows 8+, no download is necessary.
3. Open a command prompt.
4. Run "cd %APPDATA%" to go to your AppData\Roaming folder.
5a. If Windows Vista or 7: \path\to\junction.exe "%APPDATA%\Paragon Chat" "\path\to\cloud_paragon_chat_location"
5b. If Windows 8+: mklink.exe /j "%APPDATA%\Paragon Chat" "\path\to\cloud_paragon_chat_location"
* Theoretically Windows XP also supports directory junctions, but I haven't tried this on XP.