This might look like a hack, but you can try imitating to the user that he is typing in the textarea, whereas he would actually be typing in the textinput which is at the position for the next word in a textarea.Once the user selects a suggestion from autocomplete or hits enter or space inside this overlaid textinput, you can remove the text-input with the current word inside the textinput appended to the textarea.
For an autocomplete in text-input you can use on plugin from the plethora of plugins available for jquery.
