I tried this and it works for me.
<Window x:Class="TryResponses.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" xmlns:vm="clr-namespace:TryResponses"
xmlns:system="clr-namespace:System;assembly=mscorlib"
Title="MainWindow" Height="350" Width="525">
<Window.Resources>
<vm:MainWindowViewModel x:Key="MainWindowViewModel" />
</Window.Resources>
<Grid Background="LightGray" DataContext="{StaticResource MainWindowViewModel}">
<Grid.Resources>
<Style TargetType="ListViewItem">
<Style.Triggers>
<Trigger Property="ItemsControl.AlternationIndex" Value="0">
<Setter Property="Background" Value="LightBlue" />
</Trigger>
<Trigger Property="ItemsControl.AlternationIndex" Value="1">
<Setter Property="Background" Value="LightGray" />
</Trigger>
</Style.Triggers>
</Style>
<DataTemplate DataType="system:String">
<!-- put your data template here -->
</DataTemplate>
</Grid.Resources>
<ListView ItemsSource="{Binding Items}" AlternationCount="2" />
</Grid>
I hope this will help.
Regards
Claude