Use x-webkit-speech with a textarea
Currently it only works on inputs. I assume that support for longer text entry will come eventually, but as users might expect to record much longer entries I suspect they were worried the accuracy and time for processing would be affected.
The answer is fairly straightforward: add a text input box above your text area and then use the onwebkitspeechchange attribute to cause the newly recognized text to be copied from the input box to the text area.
I have posted a code sample on jsfiddle: