Difficult but not necessarily ASB
The most probable avenue would be a duplication of the hox genes.
Beat me to it. It's hox gene duplication. Gotta fool around with what segments go where.
Hopefully, this won't screw up the rib cage too much, or cause irreprable damage to internal organs.
Let's think of a plausible way this could happen without risking that kind of a problem.
It's been too many years since developmental biology. If I remember right, limb buds are a matter of a dorsal-ventral signal gradient interacting with the segment identifier. Maybe the promoter for the limb bud signal gets a segment tacked on that responds to the d/v gradient at the wrong segment. This could be due to wacky transposons, poor recombination during meiosis 1 or a retrovirus. (oh those wacky transposons!) Radiation-induced mutation is... more unlikely. That should do the job without directly harming internal organ development.
There you have it gentlemen: Non-asb 4-armed humans. Now get them to reproduce consistently. They'll have poorer health and coordination. Maybe they're considered sacred, like albinos are some places in Africa. Will 4-armed priests conduct sacrifices at the Great Pyramid of Mexico?
(The Unconquered Sun FTW!)
The longer you keep these fellows going, the healthier their 'special attribute' will be. The rest of the genome will adapt, just through natural selection, to cause the extra arms to have less negative impact on health/survivability. EDIT: Just looked it up- the vertebrate limb inducer is a dash of FGF-10 at the right time.