Adding a class to wordpress gallery code

Is there any way I can add a small snippet of code to the wordpress generated gallery image links?

All I want is for the wordpress gallery links to generate the <a> links with a class section such as follows:
<a class="img_frame" .../>

I know there are plugins to create other image lightboxes, but those create an incompatibility with my current theme. My theme has its built in lightbox, but it does not work with the native wordpress galleries. I have searched through a ton of wordpress core files to try and find this, but pretty much came up empty handed with my limited php know how.

Thanks you anyone that can give me some insight.