How to serialize an object using JFileChooser

Question

I want to use the JFileChooser to create a dialog box to save my 2 by 2 Array as a serialized object.

This is the code I have used previously to serialize objects and it works fine however, this just generates the file and puts it in the same directory as the program. I want to use the JFileChooser to choose the location of the saved file.

private void serializeMap() throws IOException {
    File file = new File("map.txt");
    FileOutputStream fos = new FileOutputStream(file);
    ObjectOutputStream oos = new ObjectOutputStream(fos);
    oos.writeObject(grid);

    oos.close();
  }

So far this is all I have.

private void exportMap() {
    KeyboardFocusManager.setCurrentKeyboardFocusManager(new DefaultKeyboardFocusManager());
    JFileChooser fileChooser = new JFileChooser();
    fileChooser.setSelectedFile(new File("map.txt"));
    fileChooser.showSaveDialog(this);
    KeyboardFocusManager.getCurrentKeyboardFocusManager().addKeyEventDispatcher(gameKeys);
  }