I agree with the comments that radio buttons would be the usual UI element when only a single item is 'checked', but if you want to stick with a CheckedListBox for your UI, you can try something like this:
private void checkedListBox1_ItemCheck(object sender, ItemCheckEventArgs e)
{
CheckedListBox.CheckedIndexCollection checkedIndices = checkedListBox1.CheckedIndices;
if (checkedIndices.Count > 0 && checkedIndices[0] != e.Index)
{
checkedListBox1.SetItemChecked(checkedIndices[0], false);
}
}
You also might want to set CheckOnClick to true for the CheckedListBox.
Edit
Updated the code per your comment to deselect an item if it is unchecked. The problem is that unchecking the previously checked item causes the event to fire again. I don't know whether there is a standard way to handle this, but in the code below, I detach the handler before calling SetItemCheck, then reattach the handler. It seems like a clean way to handle this, and it works. If I find that there is a recommended way to handle this, I will update my answer.
HTH
private void checkedListBox1_ItemCheck(object sender, ItemCheckEventArgs e)
{
CheckedListBox.CheckedIndexCollection checkedIndices = checkedListBox1.CheckedIndices;
if (checkedIndices.Count > 0)
{
if (checkedIndices[0] != e.Index)
{
// the checked item is not the one being clicked, so we need to uncheck it.
// this will cause the ItemCheck event to fire again, so we detach the handler,
// uncheck it, and reattach the handler
checkedListBox1.ItemCheck -= checkedListBox1_ItemCheck;
checkedListBox1.SetItemChecked(checkedIndices[0], false);
checkedListBox1.ItemCheck += checkedListBox1_ItemCheck;
}
else
{
// the user is unchecking the currently checked item, so deselect it
checkedListBox1.SetSelected(e.Index, false);
}
}
}