One option would be to use the phrase 'Please select a thing' as a label above the field, and to include a 'blank' (as in empty) option in the dropdown or a "none".
That way a user could select an option, and if they change their mind they can select the 'blank'/"none" option again.
I would say one possible advantage of using a blank option, is that when the user scans over their entered information, it is easier for them to see that they have not entered a selection for this dropdown. It quickly and easily visible as an empty field, as there is no placeholder text in the field.
This of course depends on implementation, and whether you want a label above the field.
As for the 'X', I would lose it (certainly in my above suggestion), and if you really want it, change it to a small text link that says 'clear selection' or something similar.