In general, don't mix Swing (and in a less measure AWT) with Processing. They have different threading model that don't mix well.

some days ago i had the same problem with the filechooser - the sketch stopt running.
im actually not that familiar with problems of mixing swing and awt, but i used JFileChooser over the awt's FileDialog for some reasons. (multiple file selection, folder selection, better control over extensions,...).

btw. i just saw, that processing also mixes JFileChooser, and FileDialog:
PApplet.java, line 5486.

public String selectFolder(final String prompt)



anyway, this is how i did it in the end:

1. import javax.swing.JFileChooser;
2. import javax.swing.SwingUtilities;
3. void setup() {
4. }
5. void draw() {
6. }
7. String file_name;
8. JFileChooser file_chooser = new JFileChooser();
9. void openFile() {
10.   try {
11.     SwingUtilities. invokeLater(new Runnable() {
12.       public void run() {
13.  
14.         int return_val = file_chooser.showOpenDialog(null);
15.         if ( return_val == JFileChooser.CANCEL_OPTION )   System.out.println("canceled");
16.         if ( return_val == JFileChooser.ERROR_OPTION )    System.out.println("error");
17.         if ( return_val == JFileChooser.APPROVE_OPTION )  System.out.println("approved");
18.         if ( return_val == JFileChooser.APPROVE_OPTION ) {
19.           File file = file_chooser.getSelectedFile();
20.           file_name = file.getAbsolutePath();
21.         } else {
22.           file_name = "none";
23.         }
24.       }
25.     }
26.     );
27.   }
28.   catch (Exception e) {
29.     e.printStackTrace();
30.   }
31. }
32. void keyReleased() {
33.   if ( key == 'o') {
34.     openFile();
35.     println( file_name );
36.   }
37. }

That's a smart solution. Others chose to invoke noLoop() before opening the JFileChooser, then calling back loop() on return: thus the draw() loop is stopped and there is no interference.