I found a workaround, by recreating the chart when the window resizes.  I use a DispatcherTimer to delay things a little to limit the times the chart has to be recreated.  I had to set RefreshEnabled to false in the Chart Loaded handler, since setting it when I create caused the chart to not render correctly.  Seems to work pretty well, but obviously I'd prefer to not have to pay the expense all the time.

Here's the code in case anyone else is hitting this:

XAML:
-------

<Grid >
    <Grid.RowDefinitions>
        <RowDefinition Height="*" />
        <RowDefinition Height="50" />
    </Grid.RowDefinitions>   
    <Canvas Grid.Row="0" x:Name="CanvasWindows" />
    <StackPanel Grid.Row="1" x:Name="PanelMinimized" Orientation="Horizontal" />       
</Grid>

Code behind:
--------------

public partial class ChartWindowTest : UserControl
{
    DispatcherTimer chartTimer;
    private XamWebDialogWindow chartWindow;
    private List<KeyValuePair<string, int>> data;

    public ChartWindowTest()
    {
        InitializeComponent();
        this.Loaded += new RoutedEventHandler(ChartWindowTest_Loaded);
        this.chartTimer = new DispatcherTimer() { Interval = TimeSpan.FromSeconds(0.5) };
        this.chartTimer.Tick += ((s, e) => {
            CreateChart(null);
            this.chartTimer.Stop();
        });
    }

    void ChartWindowTest_Loaded(object sender, RoutedEventArgs e)
    {
        data = new List<KeyValuePair<string, int>>();
        data.Add(new KeyValuePair<string, int>("Category 1", 50));
        data.Add(new KeyValuePair<string, int>("Category 2", 100));
        data.Add(new KeyValuePair<string, int>("Category 3", 20));
        data.Add(new KeyValuePair<string, int>("Category 4", 80));
        data.Add(new KeyValuePair<string, int>("Category 5", 50));
        data.Add(new KeyValuePair<string, int>("Category 6", 100));
        data.Add(new KeyValuePair<string, int>("Category 7", 20));
        data.Add(new KeyValuePair<string, int>("Category 8", 80));

        chartWindow = new XamWebDialogWindow()
        {
            MinimizedPanel = this.PanelMinimized,
            Header = "Chart",
            Width = 200,
            Height = 200,
        };
        chartWindow.SizeChanged += new SizeChangedEventHandler(chartWindow_SizeChanged);

        this.CanvasWindows.Children.Add(chartWindow);           
    }

    void chartWindow_SizeChanged(object sender, SizeChangedEventArgs e)
    {
        var window = sender as XamWebDialogWindow;
        if (window == null
            || window.WindowState == Infragistics.Silverlight.WindowState.Minimized
            || window.WindowState == Infragistics.Silverlight.WindowState.Hidden
            )
            return;

        // Fire on timer.
        if (!this.chartTimer.IsEnabled)
            chartTimer.Start();
    }

    void CreateChart(object objectState)
    {
        var chart = new XamWebChart();
        var series = new Series()
        {
            ChartType = ChartType.Bar,
            DataMapping = "Value = Value;Label = Key",
            DataSource = data
        };
        chart.Series.Add(series);
        chart.Loaded += new RoutedEventHandler(chart_Loaded);

        this.chartWindow.Content = chart;
    }
   
    void chart_Loaded(object sender, RoutedEventArgs e)
    {
        var chart = sender as XamWebChart;
        if (chart != null)
            chart.RefreshEnabled = false;
    }
}