Upon encountering this delicate green insect, few people would immediately think "cockroach," but that is exactly what it is. The green roach (Panchlora nivea), also called the Cuban roach, is, as you might have guessed, not native to Austin, Texas. It is, however, found throughout the southern U.S., having arrived as a hitchhiker on plants, fruit, or other products from tropical areas.
Like other roaches, this one is probably a scavenger (very little research has been done on roaches in the wild), but is not one of the pest species that readily takes up residence in houses. It might be attracted to lights and accidentally enter, but in our area I find them in woodpiles and gardens. Being nocturnal, they will only be found when their daytime hiding places are disturbed, and will not hesitate to fly away, so they are a bit difficult to observe.
The green roach gives birth to live young; they are a rather large size for this small insect so it only produces a few babies at a time. I discovered this after my mother swatted one that flew into her house in Florida and a close look at the corpse revealed a baby emerging and another still inside.