Serialize? Do you mean synchronize? JSObject works by passing primitives to a single JSContext JNI NPAPI wrapper which acts on the DOM in the underlying browser implementation. Are you referring to the passing of primitives through JNI?
I don't know much about how chrome's JS engine works, but I assume that since the liveconnect NPAPI in chrome is the same as the others, the ability to write multithreaded javascript has nothing to do with multithreaded JSObject access. The affected code extends the same abstract JSObject class that firefox uses.
There are several implementations of JSObject/liveconnect -- a few for netscape/firefox and one for ie (ocx). All behave differently as far as multiple threads go.
DOM access isn't threadsafe in general as far as liveconnect is concerned. So, officially, multiple threads accessing the DOM is undefined. If you manage to actually access the DOM through something other than code scoped in DOMService.run(), you'll get crazy deadlocks and race conditions.
So, basically, you need all of your java threads to post all DOMActions to your DOM access dispatch thread only.