what kind of column is it? A picture would help.

Pressure-treated
posts with cedar wrap. Attached a picture that shows outlet location.

If using the tiny Christmas type gold string lights, just wrap them around the pillar on the way up, and add a string to wrap down a corresponding pillar to make it look even. I know, far from perfect, but ...

If using the heavy-duty café lights, tape or carefully staple the cord in a very straight, flat line going up the column. Or if that looks too tacky, just learn to live with the cord. Life comes with cords... (sigh).

Another thought -- use lights that have batteries as a power source, or solar lights. I used solar lights on my deck and they work surprisingly well. The brand is Gama Sonic and some models have as much as 130 lumens output.

anything on the face of the column is going to look like hot garbage. If you used low voltage string lights, you could pop the cap off, drop a length of 14-2 wire down the gap between block and post, and come out the bottom somewhere (ideally under the patio). Then you could run your wire to a transformer located somewhere else. If you can then pop the cedar wrap off the post, even better. Don't even use the outlet on the pillar, except for margaritas.

Scott .... wireless bluetooth lighting. Problem solved! :-)

Joking aside, everyone has already given all the possibilities. Other than deconstruction and rebuilding, I can't think of an invisible way to get a wire up to the top, unless you can supply electricity from a completely different location.

Appreciate all of the feedback and suggestions. While not
ideal, I think I might go the direction of solar lighting. That will at least
allow me to position the solar charger on the top of the pergola and keep it
somewhat out of view. Can use the outlet for the margarita machine :-)

http://touchofeco.com/edisonstyles/earlyedisons?upi=0