You can mount a tape light in a channel. For example, this TAMI LED Strip Channel is only 1/4" high. Be sure the channel is wide enough for your tape lights and the channel has a lens/diffuser to minimize reflections of the individual LEDs in the countertop.

With tape lights you will need an LED driver to adapt the lights to line voltage. These are generally small and can be mounted under the cabinet.

@ci_lantro Thank you for your reply! I'm not quite sure I understand. Would you mind giving me a link to what you referring to?

Where is the 110v run to? If it is stubbed out of the wall just tuck it up into the cabinet and put the transformer there so you can have tape lights

@wdccruise Thank you again. The 110 wire is already sticking out of the wall underneath the cabinets, awaiting non-low voltage lighting. Electrician is saying he can't convert to tape strips because walls are now closed up. And lighting guy from Lowes told me it can't be done due to code. So not really sure were to go from here. I appreciate you sending me that link but still not understanding what I would need to make this happen.

Can a light rail be added to your cabinets?

@HALLETT & Co. thank you for your reply. Yes the 110 wire is sticking out of the wall, underneath the cabinet, awaiting non low-voltage lighting. Would you mind sending me a link for a transformer that would work for this situation? I am not really clear on what I need.

@vinmarks Thank you for your reply. This is not an option for us (time, money, etc.) but thank you for the suggestion.

"The 110 wire is already sticking out of the wall underneath the cabinets, awaiting non-low voltage lighting. Electrician is saying he can't convert to tape strips because walls are now closed up. And lighting guy from Lowes told me it can't be done due to code."

This doesn't make any sense. You would need four things:

1. Tape lights: long enough to run the total length* of the undersides of your cabinets, width that will fit inside the channel, appropriate color temperature for a kitchen (e.g., 3000K to 3500K IMO), and appropriate brightness.
2. Aluminum channel: Shallow channel with diffuser/lens into which the tape lights would be placed.
3. A hard-wire power supply/driver/transformer: To convert the 110 volts to 12 or 24 volts required by the tape lights and hard-wired to the 110 cable sticking out of the wall. Driver should be dimmable and controlled with a compatible wall-mounted dimmer. Depending on the cabinet, you may be able to attach the driver to the underside of the cabinet or drill a hole in the bottom of the cabinet and put the driver inside.
4. Various wires and connectors to connect the LED tape light segments together and to the driver.

*If cabinets are not continuous, you'll cut the tape light into segments and wire the segments together.

Not sure where you are, but maybe you can find similar lights. These are from Menards (a big box store in the MIdwest.) They are a super slim design, motion activated. Plug in, not direct wire, but you could change your 110 wire to an outlet, maybe inside a cabinet.

Patriot Lighting® Slim LED White Plug-In Motion Sensor Under Cabinet Strip Light at Menards®

Patriot Lighting® Slim LED White Plug-In Motion Sensor Under Cabinet Strip Light at Menards®

My husband installed the above lights, linked together, and ran the plug in end through carefully drilled holes in the bottom of the cabinets where it does NOT show.

Undercabinet lighting has to be planned from the beginning, or you end up with a not so pretty solution.

@Mary Elizabeth: "These are from Menards (a big box store in the MIdwest.) They are a super slim design"

How thick are these lights? Most are about one inch, vs 1/4" for the LED tape-light channels linked above.

I don't know where you are that you have DC wiring in your house - I'm not an electrician but I thought the standard in the US was 110V AC

Anyway, my undercabinet lights are direct wired (they came with plugs but were convertible, which the installer did easily) are 5/8". They are Utilitech brand from Lowe's. EIght years ago, so the models have likely changed a bit. Similar to THESE

Don't be confused by "depth" in the description - that is front to back, not top to bottom.

Home Depot also has well rated similar light bars.

LED driver 8"L x 1 3/16" W x 3/4" T

LED tape light stuck to bottom of cabinet without using channels.

I needed something quick & cheap so didn't fuss with the channels. Made sure to buy tape lights with 3M brand adhesive. Have been in place for +/- 5 years.

I have plans to finesse the install but obviously not high priority. :-) .

30 watt LED Driver/ Power Supply/ Transformer for strip lights

@raee_gw zone 5b-6a Ohio: The light linked above is 1-1/4" thick (listed as "height" in the specs).

WDCCRuise, so it does. I didn't read closely, just looked for one similar to mine.

It seems that the ability to adjust color temp and other features are reducing the availability of slim ones like mine. And, they are much more expensive, too.

Home Depot does have one under 3/4" though.

@wdccruise, the website description lists the size of the packaging (as if anyone cares!). The lights come in 12, 18 & 24 inch lengths. They are 1 1/2" wide and less than 1/2" thick, & completely hidden under most cabinets.

I'm rather OCD with these kind of details, so I had these picked out before any electrical, sheetrock, or cabinets were installed.

@ci_lantro: "LED tape light stuck to bottom of cabinet without using channels."

The only risk of not using channels with diffusers/lenses is that you might see the individual LEDs reflected in the countertop if you have one made of a shiny material.

I had flouresent lights under my cabinets and they hung down and were visible and we had to replace the bulbs frequently. My son put in puck lights and now it looks great and are not visible from the front. They are continuous wired and turn on with one switch.