Wind and rain carried the radioactivity across western Europe, contaminating soil.
Wild boar are thought to be particularly affected because they root through the soil for food, and feed on mushrooms and underground truffles that store radiation. Many mushrooms from the affected areas are also believed to be unfit for human consumption.
Since 2012, it has been compulsory for hunters to have wild boar they kill in Saxony - about 1125km from Chernobyl - tested for radiation. Carcasses that exceed the safe limit of 600 becquerels per kg have to be destroyed.
Now, in one year, 297 of 752 boar tested in Saxony have been over the limit, and there have been cases in Germany of boar testing dozens of times over the limit.
The radioactivity is causing economic problems as well. Many hunters sell the meat, and the German Government is having to pay thousands of euros a year in compensation to hunters whose kills have to be destroyed.
"It doesn't cover the loss from game sales, but at least it covers the cost of disposal," Steffen Richter, head of the Saxon State Hunters Association, told Bild newspaper.
Based on the tests, experts predict the problem could continue for 50 years.