Yes. Root rot is common with starting chestnut from nuts in containers. I don't know much about the pathogen involved. In post mortems it is not uncommon to find a swollen root that is almost carrot like. The culprit is watering technique that encourages whatever the pathogen is. Typically is it watering too frequently.
I can't tell what kind of container you are using but you need to start with 18s to get the tap root pruned in the first 4" Perhaps you just transplanted them. You can't water on a schedule because conditions vary as they trees grow. I find the best method is to water by weight. Fill the container with medium (promix or whatever you are using. Don't use an off the shelf mix like miracle grow that is designed to retain water. Use a well drained mix like promix or equivalent). Then pick up the container and get a feel for the weight. This is how empty feels. Next saturate the container with water until it is running out the lowest holes. Now lift the container again and get a feel for weight. This is how full feels. Typically you want to completely saturate when you water and then let everything dry out. When the weight of the container tells me we are about at 1/4 tank, it is time to saturate again. If you ever see the leaves begin to droop, water immediately. They should stand back up in a couple hours. You can't use too much water at one watering but you can water too frequently and that is common. This method works with any size container. Keep in mind they will become hard top-water. You have to apply water a little at a time and let it soak in until it comes out the lower holes. This is because the well drained mix has lots of voids. As the root system develops it fills these voids and water infiltrates much slower.
Another possible problem. I can't tell from the pics if you are using artificial lights or not. If not, they are doomed anyway. Whitcomb warns about getting anxious and trying to start trees early in a green house. They will look great above the soil but the low intensity and low angle of the sun cause very poor root system development. They become very leggy. One year another guy and I started trees in rootmakers. He started his in a greenhouse and I started mine under fluorescent lights hung a few inches above the trees. We started them at the same time and they looked about the same above ground. When it came time to transplant his had very tiny root system and many died. Mine had great root systems. Putting them in an indoor green house near a window is fine but you need artificial lights as well in the winter. You don't have this issue with direct seeding because the trees just won't grow until the sun is high enough in the sky because of the temperature outdoors. They just wait to germinate and grow.
Hope this helps,
Jack