Let the electrician figure it out and give you a price. That is his responsibility. If you don't like his price, get 2 or 3 more and compare. That is your responsibility.

I'm by no means an expert, but I think for the undercabinet lights, you want the electrical cable poking out from the drywall before the cabinets are installed, toward the bottom of where the cabinets will go, but still within the footprint of the cabinet (above the backsplash).

Then, drill 1/2" holes in the back of the cabinet and the bottom, and feed the cable from the wall through the back as you hang the cabinets. Once the cabinets are hung, install an outlet inside the cabinet, and feed the cable for the lights through the bottom hole and plug into the receptacle (assuming your lights are not intended to be hardwired).

As to cost, I think people would need more info to get an idea.

Do you trust your contractor? As btharmy said, let them figure it out and give you a cost. Unless we're missing some key info, this should be a pretty easy task.

Thank you both!

Nice explanation emcloud.

Would that be ONE installed outlet in a cabinet for that side run of UC lights? Not one outlet per cab, yes? One GC told me one outlet per upper box, I said later.

You can daisy chain from cabinet to cabinet in the wal to interconnect.

Power goes in one end of each section, exits the other end, loops back into the wall, then forward and into the next section.

you could do it on the bottom of the cabinet if the AHJ does not mind the exposed NM and you are wiling to drill the bottom edge of each cabinet for the cable.

You can do it on the bottom of the cabinet with smaller holes if you can find smooth jacketed MC (Metal Clad) cable.

In #14 smooth MC is about 1/4 inch diameter (2 wires with the jacket as the ground).
You will need to find clamps compatible with MC for grounding and also with plug mold (this may be difficult).

You could go as far as notching the bottom edge of every cabinet wide enough to pass the plugmold and use a single long piece, or block it down on wood to miss the cabinet bottom edge (might be OK with a big enough light apron on the cabinet bottom).

A combination of notching and spacing could also be used.

The short missing section is not going to significantly weaken the bottom of the cabinet.

brickeyee, thanks for the above.

If you would, might you comment for the OP and us on distance from countertop to bottom of light rail adjacent to a (gas) range? I assure you, this is not a trick question, but one seeking input on your take of most range manufacturers requirement of 18" from cooking surface to nearest adjacent combustible surfaces. I'm stumped whether to omit light rails, as my semi-custom cabinets need to be parallel in height at least, so best be at 18" above counter.

Also, there's an active thread on this over in the KF, you might comment on too.

18 inches to flammable items would include light rails/aprons if they are wood.

The AHJ is likely to miss it though.

Expanding on EMcloud's response, the LED strips and bars are low voltage so the electrical connections would be low voltage wiring back to a central transformer. The central transformer will drive the low voltage LED bars.

I have LED under cabinet bars from environmental lights and that are powered from a single transformer that is connected to a switched outlet controlled by a dimmer switch. In my case the outlet and transformer were hidden in one of the cabinets.

The electrician ran low voltage wiring from the transformer to the under cabinet location as described by emcloud. The final connectors were spliced to the low voltage wiring. The entire kitchen was about 50 watts of LED bars.

"low voltage wiring back to a central transformer."

Often a painfully expensive way to do the job.
Low voltage requires higher current and low voltage drops in conductors, requiring the use of larger wires.

60 W AC to DC supplies are around $15 each and fit in a single gang box.
120 VAC in one end, 12 VDC out the other.

You can cut through the cabinet back, mount a device box flush with the inside of the cabinet back, then use a blank switch-plate on the box.

The 12 V lines exit through the bottom side of the box, through the bottom of the cabinet, and then to the nearby lights.
Repeat as required.

If a single large er transformer fails ALL the lights are out.

If a single AC-DC power supply fails all you lose is (up to) 60 W of lights.

It works especially well with 20 W pucks.

3 pucks per supply.

You can even use another low voltage supply (24 VAC, power limited) with relays to switch the segments.

Same sort of scheme as a thermostat, with all the wiring relief these circuits have (and common and inexpensive transformers and relays from the HVAC world).

You may need to use as 4x4 box with a single gang plaster ring to fit power supplies and relays.