This is so easy now that I know how to do it, but I didn’t realize that fields could be themed similar to nodes.
Just create a template file titled:
field–[field_name].tpl.php
and save it in your theme’s directory:
/sites/all/themes/[your_theme]/
You can get the field name on the Content Type screen, Structure > Content types > [your_content_type]
Then you just enter your markup in the field–[field_name].tpl.php file that you’ve created.
You can use the field.tpl.php file located in /modules/field/theme/field.tpl.php as a starting point.