How to do it...

Jira uses Velocity templates to render custom fields. These templates are mostly HTML, with some special symbols. You can find all these files in the JIRA_INSTALL/atlassian-jira/WEB-INF/classes/templates/plugins/fields directory, and the edit view templates are in the edit subdirectory:

Open the edit-select.vm file (located in the previously mentioned directory) in a text editor, and remove the following code snippet:

#if (!$fieldLayoutItem || $fieldLayoutItem.required ==  false)  
 <option value="-1">
  $i18n.getText("common.words.none")
 </option> 
#else 
 #if ( !$configs.default ) 
  <option value="">  
   $i18n.getText("common.words.none") 
  </option> 
 #end 
#end

Save the file and restart Jira. Make sure you do not change any other lines.

You can remove the None option from other custom field types, such as multi-select, by editing the appropriate file (for example, edit-multiselect.vm).