JFileChooser: checkbox selection

I'm currently trying to automate regex usage (match/replace-pairs) on a huge number of files by writing a small application that allows the selection of files, regexes, etc. Therefore, the user should (obviously) be able to select files, a purpose for which I am using the JFileChooser provided by javax.swing.JFileChooser.

Now, while this is basically working so far, I would like the selection to be via checkboxes, as possible in the default windows explorer (see screenshot below).

Is this possible with the default JFileChooser? Or would I have to write a (for this purpose potentially too complex) custom JFileChooser?

Any help appreciated!