Such a difficult question! I ought to know. This is the situation I am in. I have filed. In my case, this was not just one offense. Even though this was the first "technical" adultery, i.e. the first in-flesh fornication (that I know of!), there have been years of infidelity in one form or another, e.g. viewing of pornography, visiting strip clubs, socializing with women w/out me.
I found out about all these things very much after the fact, as I was lied to for many years, beginning during our courtship. There was much emotional and psychological abuse. He has no respect for me. I hung in there all this time and worked my hardest to make things better, including making him go to marriage counseling, because I personally believed it was my duty due to the covenant I had made with God. ...but this for me was the last straw, and by God's merciful permissive will, this choice is provided for in scripture. I hope you have not suffered in this way, but if you have....as excruciating as I know it is....have courage to leave him. Maintain your self-respect while you still can.
Hold him accountable for his actions, once and for all. If he truly changes and becomes a reformed person, it will become obvious, and perhaps you can one day reconcile. If he doesn't...well, then, you are better off. Now, if on the off chance that you have had a very healthy marriage and this was, as far as you know, a single transgression (...rather than a relationship or multiple cases of adultery. In my husband's case.. this was a six month emotional attachment and relationship, involving much debauchery, too), it would of course be desirable to God if you could reconcile, particularly if there are children involved. ..but seek wise counsel. His true remorse and commitment to real change is imperative. Either way, seek counsel for yourself. The trust that has been breached will take years to rebuild. Above all, be good to yourself. There is NO excuse for his choice. God bless.. and be strong.