How to extract a single frame from a live photo?

If you upgraded to macOS Sierra by now, you can simply export the Live Photo from Photos with "File > Export > Export unmodified original".

This will export a video and a still frame. Delete the exported still image, but rename and reimport the video part. Now you have a regular video and extract any frame as a still image from the video. Then delete the video again.

To create a still frame, select the video in Photos, double-click it to enlarge it. Use the video controls to advance to the frame you want to export as a still image.

Click the gears icon with the actions menu and select "Export frame to Pictures":

You will find the still frame in the Pictures folder. Drag it onto the Photos icon to import it to your library.

There is no support in Photos for Mac for this, but you could try the app Splitter - For Live Photos on your iPhone to extract the video part. Then you can extract any frame as a still photo from the video.

The still frames from the video wll have poor resolution compared to the embedded, high resolution still image, however.

I use app Lively & it works great for this. Has option to

save a frame

You could take a screenshot while the Live Photo is playing in full screen mode.

Use the key combination ⇧⌘3 to capture the screen.