How do I delete a local branch on Github Desktop?

On Mac OSX:

for everyone having this problem with the latest version: Select the branch that you want to delete, go to "Branch" -> "Delete Branch"

On Windows:

Here's the answer I got from github CS when I contacted them about this:

Thu 2015-08-13 3:38 PM Hi Daniel, Sorry about that! We'll be adding the option to delete branches back in an upcoming release. For now however, here's how you can delete a branch from the Git Shell: Hit ~ in GitHub Desktop to open up the repository in the Git Shell Run 'git branch -d branch_name' When you create a new branch you should see an option to publish it directly in the comparison graph. Let me know if that doesn't make sense or if you have more questions - thanks and sorry for the inconvenience! Robert

I've noticed there is a delay (about 2 or 3 minutes) between deleting the local branch in the shell and git desktop realizing the change.

UPDATE

In 3.0.5 They added Delete the current branch from the gear menu.

In GitHub Desktop, you can delete the current branch here:

With the following dialog allowing you to delete it from remote as well:

In desktop, make sure you are in the correct branch, and press "ctr+shift+D".This should delete the branch, this method works in windows; I cant confirm for other Linux/Mac.