The ListBox for WPF doesn't provide built-in CheckBoxes functionality, but you could easily implement it by yourself. You will need to apply ItemTemplate which contains CheckBox and TextBlock for example which TextBlock will be bound to a property in the custom object from the ListBox ItemsSource collection. As for the CheckBoxes they can be bound to the IsSelected property of each ListBoxItem, so whenever you check a CheckBox the item gets selected. Finally in order to get the checked items you could just use the SelectedItems collection of the ListBox which will contain only the selected ones. For your convenience I have prepared and attached a sample project which demonstrates the exact approach.
Hope this helps.