Slice the zucchini into 1/4-inch thick rounds. It's best to keep the thickness the same for even drying. Experiment with using a crinkle cut slicing blade that makes ridges in the chips, the ridges tend to give spices more area to grab on to.
Add apple cider vinegar, salt, pepper, and chili powder to a wide bottomed, nonreactive bowl. Stir until incorporated.
Add a handful of zucchini slices to the bowl and toss until they are just coated with the vinegar and spice mix. Separate any pieces that stick together.
Arrange the chips on dehydrator trays. They can touch but should not overlap. Repeat with the remaining zucchini slices.
Dry at 135°F for 10 to 12 hours until crisp. If you have a bottom heating dehydrator, you may need to rearrange the trays halfway through the drying cycle. After 5 hours, move the top trays to the bottom so that chips will be evenly dried.