Legal entities have been around for centuries. Ships stolen, then used for piracy, have been found guilty of crimes and destroyed. They were represented by agents, so 'facing one's accuser' was solved centuries ago. Other legal fictions include: companies, cooperatives (co-ops), coprorations, municipalities, political parties, sovereigns, states, temples, and trade unions (src: wikipedia 'Legal Entity'). And this isn't even that new of a question: Thirty years or more ago, a legal brief and book started to ask whether a tree could have standing, since it was understood that it would be granted standing if carved into a boat. In the last decade, a couple specific watersheds and ecosystems have gathered a degree of standing (seems like this was in New Zealand and Ecuador, perhaps?). This was done so that case law could form around protecting these directly, rather than forcing someone to prove their own personal damage by an abuse by another.
Each Legal Entity (aka legal fiction) may have limitations on what they're allowed, laws to govern their agents, limitations on what laws they're held liable for.
Slashdotters also easily see this becoming an issue due to technology: will technologically-created entities be granted rights? What level of tissue regeneration crosses from a 'vat grown organ' to enough sentience to earn rights? Can we clone ourselves completely to have 'hot spares', or does a sentient clone gain any rights? Similarly, several proponents of Singularity believe they'll copy themselves into code. Does the originator retain their rights and possessions? Can they 'claw back' stuff they signed away to their code alterego? Does the code alterego get any rights?
As for us not being ready, that's baloney -- If anything, an unwillingness to cause big upsets seems like a trait of an ossified and post-climax nation or culture. When we need to, we routinely write laws out of expediency. When there's big money at stake, legal challenges routinely slow progress for financial, not ethical immaturity reasons. There's no reason a legal system can't step into this 'personhood of a chimp' tangle, decide that the benefits outweigh the impacts and declare that a chimp or critter of another species has some rights, gets a guardian ad leitem (like CASA does for kids), and faces some laws/limits/penalties. Heck, in the case of endangered species, such a process could be more effective than current actions/measures. I bet we'll see other nations continue to experiment along these lines.