You sure can!
Step 1. On your vialogue’s play page, go to “Settings”, located in the menu at the top of the page.
Step 2. Navigate to the "Delete" tab.
Step 3. Choose whether you'd like to delete the entire vialogue or just the comments and then hit "Delete".
Once it's gone, it's gone for good so make sure you really want to delete it. Otherwise, consider closing your vialogue.