Hi Bill,
It is true that some great apes display specific performances that could bring  to consider that they may be self-conscious. But looking at these performances does not confirm such a perspective:
- Mirror Self-Recognition: Some birds pass the MSR (http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0060202). Birds are not self-conscious.
- Theory of mind within great apes is a highly debated subject. Even in the case of a positive answer, I do not see the ability to attribute mental states to others as being a signature of self-consciousness.
- Empathy: some modern apes exhibit empathy. But it is difficult to consider empathy as a signature of self-consciousness.
Christophe