You will need the tool "CT_Explore: Chrono Trigger Exploration Tool" by rivernyxx to apply the patch. 
    Link to download on rivernyxx's site: http://rivernyxx.com/downloads.html
    Link to rivernyxx's instructions for the tool: http://rivernyxx.com/projects/files/changelogs/36/CT_Explore%20v1.4.txt
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Abridged instructions:
    1) File -> Open Archive: Explore to the Chrono Trigger install directory and select 'resources.bin' file to open
    2) Patch -> Open CTasGaeilge.ctp (my patch)
    3) File -> Save Archive
    4) Play the game!
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Typical install directory location:
     *\Steam\steamapps\common\Chrono Trigger