Julia, I think you are going to need to use javascript to complete this task as Eloqua does not have this logic built in. Below is a thread of a solution other users have used:
http://topliners.eloqua.com/thread/7018
To explain why a picklist isn't supported at the current time think about this:
Picklist:
Select One
Option 1
Option 2
Option 3
This gets written in code as:
<select>
<option value="Select One">Select One</option>
<option value="Option 1">Option 1</option>
<option value="Option 2">Option 2</option>
<option value="Option 3">Option 3</option>
</select>
So in theory, making a drop-down "required" would even allow "Select One" to be selected from the list In order for Eloqua to allow a picklist, and what is found in most editors that allow it, is an option to "disallow the first option" when making a picklist required.