Custom Field - drop down list

I would like to have a custom field that gives the user a drop down list of choices, but that the user can also readily add to the choices. For example, the field I want is for the name of a Trade Show, which is obviously a list that grows over time. I want a drop down list to ensure accurate entry of data (ie I don't want the name of a show to be entered differently by mistake - Cooking Convention vs Cking Convention).

Is there any way to do this?

Thanks!