Of course, we must not forget the humble platypus. A mammal with the bill of a duck, the feet of an otter, the tail of a beaver, and the egg laying capabilities of non-mammals. Truly it is what most chimeras wish they could be--real.
But in slightly less seriousness, yeah it kind of depends. Most mythological creatures end up being chimeras of some kind since a lot of monsters were conceived of by combining aspects of things people knew. You end up with two distinct variations--the monstorous abomination kind. Things like baphomet, manticore or griffin or the classic alchemical created chimera show up. Since fantasy is full of natural chimeras, you end up with a secondary distinction that chimeras are created by human or human-like higher forces. On the other end, you have holy chimeras-by-definition. The sphinx would be a good example of something that is technically a chimera and seen in a relatively positive light and as a symbol of wisdom.
If you switch to real world and sci-fi, our chimeras are like the goats that produce silk. Then, you go up the ladder to the pig-human chimeras, or animals being engineered to produce human organs. In our world we see ethical concerns arise with the treatment of these creatures such that people are now starting to question the ethical concerns of disposing of these creatures.
Sci-fi would ratchet up these concerns and depict futuristic worlds which are filled with these creatures and play with various philosophical concepts such as trans-humanism VS naturalism and the nature of sentience.
Overall, I like the platypus.