The calling thread cannot access this object because a different thread owns it

Try this:

System.Windows.Application.Current.Dispatcher.Invoke(
System.Windows.Threading.DispatcherPriority.Normal, (Action)delegate
{
    // Update UI component here
    CheckBox.IsChecked = false;
});

In case you don't want to use Dispatcher for some reason, you could use SynchronizationContext. There is not much difference, but I feel less guilty when using SynchronizationContext as it's not a WPF specific class:

private static System.Timers.Timer aTimer;
private SynchronizationContext _uiContext = SynchronizationContext.Current;

public MainWindow()
{
    InitializeComponent();

    client.BeginConnect(remoteEP, new AsyncCallback(ConnectCallback), client);
    aTimer = new System.Timers.Timer();
    aTimer.AutoReset = true;
    aTimer.Elapsed += new ElapsedEventHandler(OnTimedEvent);

    aTimer.Interval = 2000;
    aTimer.Enabled = true;
}
private void OnTimedEvent(object source, ElapsedEventArgs e)
{

    _uiContext.Post(new SendOrPostCallback(new Action<object>(o => {
        if (client.Connected == true)
        {
            Console.WriteLine("Not Connected");
            CheckBox.IsChecked = false;
        }
        else
        {
            Console.WriteLine("Connected");
            CheckBox.IsChecked = false;
        }
    })), null);
}

A ui elememt can only be accessed by one UI Thread. CheckBox Requires UI Thread and your timer runs on different thread. Simple code to use Dispatcher

if (client.Connected == true)
{
    Dispatcher.Invoke(()=> {
        // Code causing the exception or requires UI thread access
        CheckBox.IsChecked =true;
    });
}

OR

if (client.Connected == true)
{
    Dispatcher.Invoke(new Action(()=> {
        // Code causing the exception or requires UI thread access
        CheckBox.IsChecked =true;
    }));
}

if you receive error An object reference is required for the non-static field, method, or property then use this

 Application.Current.Dispatcher.Invoke(() =>
 {
     // Code causing the exception or requires UI thread access
 });