I am a new Minnesota resident. My wife and I moved to Rochester January 2019.
Last fall, my son-in-law drew a prairie chicken permit. I accompanied him on his hunt. Neither of us had ever seen a prairie chicken before. We hunted for 2 days. My dog pointed/flushed 21 prairie chickens and 3 sharptail grouse. My son-in-law shot 2 prairie chickens and one sharptail. It was a great time. We hunted both public and private land. We saw the majority of birds on public land. We never saw another bird hunter. A deer hunter allowed us to hunt his private land after we saw a prairie chicken cross the road from a bean field at midday.
Many of the prairie chicken zones have plenty of public land with excellent habitat. You can use the Minnesota Recreation Compass to identify a good zone to apply. If you draw a permit, you can call the regional biologist/manager. They are very helpful.