Something about my setup is throwing a monkey wrench into the works. Consequently, I have abandoned the Client Side validation in favor of a Server Side validation.
Simply set the OnServerValidate property on the CustomValidator:
<asp:CustomValidator runat="server" ForeColor="Red" ID="cvCheckBoxList" OnServerValidate="cvCheckBoxList_ServerValidate" ErrorMessage="At least one item must be selected." />
Then, fill out the function on the custom control (where cbValue is a CheckBoxList control):
Protected Sub cvCheckBoxList_ServerValidate(source As Object, args As System.Web.UI.WebControls.ServerValidateEventArgs) Handles cvCheckBoxList.ServerValidate
Dim isValid = False
For Each c As ListItem In cbValue.Items
If c.Selected Then
isValid = True
End If
Next
args.IsValid = isValid
End Sub
This Server Side solution was found here, on stackoverflow.