TheCodeMan;
I'm betting you could do something like this if you want, though extra work is involved.
I'm betting your outlets under the cabinets are like the ones I show in the picture below (bottom red circled). I just drilled a hole through the wall on the inside of my cabinets, mounted a metal two ganged electrical box on the back wood of the cabinet. I then fished the wire to the bottom outlet. I then mounted outlets on the metal box and wired them into the bottom outlet's power source (top red circled).
You can even clamp the wire to the back of the metal box so everything meets "code".
Then just drill a small hole underneath your cabinets for the lighting (corners will "hide" the hole better) and plug them into those outlets via a lamp module.
Make sure you use the same wire that is used for the original outlets (usually 12 gauge romex).
Good luck,
BSr