To put it another way, lefties are more chimp-like

Chimpanzees who use tools, predominantly do so left-handed. So says this AP article, which cites current work by William Hopkins and colleagues:

A three-year study of 17 wild chimps in Gombe National Park, Tanzania, found that 12 of them used their left hands when using sticks to probe for termites. Four were right-handed and one was listed as ambiguously handed.
"Contrary to previous claims, wild chimpanzees show population-level handedness in tool-use," reported the research team led by William D. Hopkins of the Yerkes National Primate Research Center at Emory University in Atlanta. Population-level handedness indicates a preference for one hand in a large group.

What does this tell us about human hand preferences? Not too much. I saw a nice paper by Dean Falk and colleagues at last year's AAPA on the neural correlates of handedness; they're pretty complicated, and it's safe (I think) to say that it will be a long time before anyone understands how they develop. One simple neural correlate has long been thought to be petalial asymmetries, which were once assumed to be unique to humans. We now know that petalial asymmetries are common in hominoids. Perhaps it follows that handedness should also be widespread.

A conventional view would assume that the brain structures associated with hand preference emerged as adaptations for that purpose. Here's one story: people who were opposite-handed (i.e. lefties among humans) were slightly less able to learn important tool-related behaviors (like throwing spears) than others; they faced a (slight) selective disadvantage, and remain at lower frequency for that reason.

Maybe it's true. But then you have to account for all the lefties that are still around. If they really faced a selective disadvantage, they should be long gone. Instead, they're busily supporting Ned Flanders' "Leftorium".

So, one may turn to balancing selection: lefthandedness was bad, but lefties had some compensating advantages. Maybe they were more creative. Maybe they were artistic. It seems to me that there's a lot of grasping at straws here. Since when was being creative better, in terms of reproduction? You might as well tell a story about the adaptiveness of schizophrenia (also, more likely lefties). This is in the category of "any explanation in a pinch" rather than real science.

And on the other side of the coin, where's the evidence that lefthandedness is bad? Sure, they are more likely to cut off digits with power tools (true), and more likely to be bedwetters (also, sadly, true). They are also more easily hypnotized (could I make this stuff up?). But where's the study of spearthrowing? Knapping flint?

Then there are deeper mysteries. Why is left-handedness twice as common in men than in women? Why are the patterns of brain activity related to handedness different in men and women?

It's a puzzle. I may follow up later. In the meantime, I think it would be fun to train a chimpanzee to hold her termite stick up in the air, and say, "Aha, but I am not lefthanded!"