Remove the shackle and the thimble from the rope rode. Splice the rode to the last chain link. The articles above or youtube videos are good resources for the splice. The splice will go through the windlass without having to remove the "Simpson-Lawrence" cover. It does look like time for a new rode though.....that one looks very degraded.
Also, the gypsy will retrieve the rope rode as well as the chain. You don't have to wrap the rope around the capstan (the part that looks like a winch drum) to retrieve the anchor.