prova in questa maniera! dovrebbe andare!

ciao

public class Client_Interfaccia extends JFrame {
...
private JTextArea chat;
private JPanel tablePanel;
private JScrollPane barreChat;

public Client_Interfaccia() {

JPanel panel = new JPanel();


chat = new JTextArea();
chat.setPreferredSize(new Dimension(560, 200));
chat.setLocation(20, 40);
chat.setEditable(false);

barreChat = new JScrollPane(chat);

panel.add(barreChat);

this.setContentPane(panel);

resize(900, 600); // Dimensioni layout
show(); // Mostra la finestra
}