Question: I have a single select drop down and need to enable the user to clear his selection too.

Is it elegant to do this:

[![enter image description here](https://i.stack.imgur.com/UgB2z.png)](https://i.stack.imgur.com/UgB2z.png)

Or, on selection of an option should the drop down be hidden, showing the selected items text along with the `X` mark beside it clicking on which the drop down would be shown again?

Answer: 
The phrase 'Please select a thing' implies that the user has not selected anything from the dropdown yet. To clear a selection, you can have two alternatives:

1. Add a 'Clear selection' choice in the dropdown.
2. Allow the user to switch back to 'Please select a thing' which will imply that the selection previously made has been undone.

The [x] next to your dropdown confuses me. It seems like it would remove the entire dropdown, instead of just clearing the selection. My suggestion would be to use the dropdown itself for clearing options, staying within recognised UI patterns.
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.