Roy, do you know if it is a bird nest or a squirrel nest and whether it is active? If it is not active, you can certainly take the tree down. If it is a bird nest, I would do everything possible to wait until after the hatchlings fledge.
First, try to save the tree and the nest. Takes a long time to kill a tree with damage even at the base. Sometimes, the base will heal on it's own if it's just the bark pulled away or chipped by a mower or tractor.
If that's the case don't spray anything on it but do keep it clean/clear of debris where fungus/bacteria may allow for more damage.
If the base has the bark buckling around the base for no apparent reason (at the root collar) where it flares out, you may have planted that tree a little too deep or may have too much mulch in that area. If that's the case, expose more of the collar and see if the tree improves over the season.
As a last resort... I'm with Douglas about taking it down.
If you want to help the tree to live paint the wound with some cheap diluted latex paint. That will keep bugs and disease from attacking the tree through the opening. If you aren't sure about that and don't mind spending the money you can get a professional wound sealer from a nursery and paint the wound with that. It should be sealed in either case not just kept clean.
@Paul M There is a special sealant made especially for trees that can be bought at most home centers(Home Depot). just spray it on according to directions, & it will seal the wound on the tree permanently. Not sure of the cost, but I think it's around $5 per spray can.
I have rules that I go by for things like this.
#1) Check to see if the nest is active.
doesn't matter what kind of bird/animal nest it is.
#2) If it is active, wait for the babies to grow first. few things in life are worse than a baby animal/bird losing its home.
#3) If it's not active take down the tree asap. you do not want to wait till it's convenient for you because you risk some animal/bird making that nest active.
once the tree is down, then you won't have to worry any more.
Do not kill the tree!!!!!!!!
Use special tree paint for wound