In this statue there is something what looks like a face on Athena's chest. I have seen it on some other statues of Athena. What is it? Is there a myth behind it?
It's not clear from your picture, but the face is most probably a Gorgoneion, a recurring element of Athena's iconography:
In Ancient Greece, the Gorgoneion (Greek: Γοργόνειον) was a special apotropaic amulet showing the Gorgon head, used most famously by the Olympian deities Athena and Zeus: both are said to have worn the gorgoneion as a protective pendant. It was assumed, among other godlike attributes, as a royal aegis to imply divine birth or protection, by rulers of the Hellenistic age, as shown, for instance, on the Alexander Mosaic and the Gonzaga Cameo.
Source: Wikipedia contributors. (2018, June 16). Gorgoneion. In Wikipedia, The Free Encyclopedia. Retrieved 21:22, February 5, 2019, from https://en.wikipedia.org/w/index.php?title=Gorgoneion&oldid=846161112
The ever-so-helpful theoi.com has tons of information on the mythology of the Gorgons, if you wish to know more about them. We also happen to host some very interesting questions about Medusa and her sisters on this site.