"Humans experienced a brain expansion after they developed stone tools to augment their rather pitiful natural endowments. What provoked that shift?"

They weren't starving as much?

"Chimps hunt without stone tools so it wasn't hunting by itself that caused the change. Some 2.8 mya a supernova seems to have gone off close enough to the solar system to shower the planet in iron-60 and probably battered the place with cosmic-rays - chimps and gorillas seemed relatively untouched, but seemingly coincidentally Australopithecus garhi appears 2.6 mya with Oldowan stone tools. Then genus Homo springs forth at 2.4 mya. "

You have to go pretty far back to get human brains the same size as chimp brains- I think further back than 3 million years.
Oh, here:

"Scientists have unearthed the oldest child ever discovered—the fossil remains of what appears to be a girl dating back 3.3 million years.
...
This skeleton for the first time shows what an Australopithecus afarensis child looked like. This has yielded clues to how "our earliest ancestors grew their brains," said researcher Fred Spoor of University College London.

The infant's brain size is estimated at 330 cubic centimeters. This is not much different from that of a similarly aged chimp. However, when compared to adults of her species, she had formed only between 63 and 88 percent of her adult brain size. This is relatively slow brain growth compared to chimps, which by three years of age have formed more than 90 percent of the brain. This rate of brain growth is actually slightly closer to that of humans, possibly pointing to an early shift in human evolution."
http://www.livescience.com/health/060920_ancient_girl.html

I would say that a chimp has a large brain, and when I say aliens having large brains I mean something like chimp size or larger.

And obviously entire body mass is related to this, so a small creature with a chimp size brain could have more "brain power" than a human. And how the brain is designed/organized is also a significant factor. And much of what we would assume is intelligence, has more to do with software [culture] and personal motivation and "interests" than the quantity of brain meat.