Here are some links to dealing with Chara and a similar plant (alga: Nitella).
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=265722#Post265722

Identification - pictures:
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=226903#Post226903

Pictures and Control Cutrine Plus granular
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=263626

Control Methods and G.Carp not eating it well (from PBoss Q&A Achives)
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=33329#Post33329

GC eating it:
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=35230

Chara in winter:
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=265727&#Post265727

FA (filamentous algae) on Chara:
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=25228

FA and Chara - Green Clean (peroxygen carbonate aka Pak 27 and Phycomycin)
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=35162