I don't think DEET helps with chiggers unless you spray it on your underwear in the morning while getting dressed.
As I said, I spray it on my legs up to the underpant line (usually when I get to the base of the first climb of the day). This is when I am wearing shorts, by the way. It works for sure.
The DEET has to go at possible entry points, not on your underwear. (For example, the week before when I forgot to DEETify, I got bites at the back of my knees as well as at the underpant/harness lines.) If you are going to lie down in the grass, you'll need it on your upper body too.
I've been told that Flowers of Sulphur, a sulphur powder obtainable from pharmacies, also repels chiggers. Instead of the chemical DEET smell, your usual cologne will be enhanced with the delicate odor of rotten eggs.