Uncheck checkbox when another is checked

I have two checkboxes. When I check one, I want the other to uncheck if it's currently checked. Both can be unchecked. Currently, I can check one, but when I check the other, both of them uncheck. I'm having trouble figuring out why.

Note: I want to do this all in the .xaml if possible. I've been messing with data triggers to get the proper effect with no luck so far.

<CheckBox Name="SYOChkBox">
    <CheckBox.Style>
        <Style TargetType="CheckBox">
            <Style.Triggers>
                <DataTrigger Binding="{Binding IsChecked, ElementName=UTMChkBox}"
                             Value="True">
                    <Setter Property="IsChecked"
                            Value="False" />
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </CheckBox.Style>
</CheckBox>
<CheckBox Name="UTMChkBox">
    <CheckBox.Style>
        <Style TargetType="CheckBox">
            <Style.Triggers>
                <DataTrigger Binding="{Binding IsChecked, ElementName=SYOChkBox}"
                             Value="True">
                    <Setter Property="IsChecked"
                            Value="False" />
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </CheckBox.Style>
</CheckBox>