WPF CheckBox TwoWay Binding not working

You need to raise the PropertyChanged event when you set Foo in your DataContext. Normally, it would look something like:

public class ViewModel : INotifyPropertyChanged
{
    private bool _foo;

    public bool Foo
    {
        get { return _foo; }
        set
        {
            _foo = value;
            OnPropertyChanged("Foo");
        }
    }

    public event PropertyChangedEventHandler PropertyChanged;

    protected void OnPropertyChanged(string propertyName)
    {
        var propertyChanged = PropertyChanged;
        if (propertyChanged != null)
        {
            propertyChanged(this, new PropertyChangedEventArgs(propertyName));
        }
    }
}

If you call Foo = someNewvalue, the PropertyChanged event will be raised and your UI should be updated