Can I ever trust him again? Is it possible to make this work?

[Alhaja]

I've been with my boyfriend for around 9-10 months now. I love him very much and he is always kind and respectful to me.
Very early into our relationship, about one month after we started seeing each other, we were exclusive but had not made the boyfriend-girlfriend step yet. I found out he was flirting with his ex and one other girl online (they live very far away). I was upset, but mostly confused, because I didnt know what the status of our relationship was. I confronted him about it, and we got over it pretty quickly. Soon after, we made the relationship official and things were going well.

Recently, I just found out he had had another contact with his ex online that was totally inappropriate and flirty. However, the incident occurred over 6 months ago (so about 3-4 months into the relationship). I decided not to confront him about it, because I didnt want him to know that I was snooping, and because as far as I could tell he hadn't had any other contact with her since then. It looked like it was just a few minutes of inappropriate conversation, and he has been a very good boyfriend since.
During the past 6 months, our relationship has grown and strengthened a lot. We have been very happy with each other, and he finally started telling me he loves me (a very big step for him). I believe that his feelings for me are genuine.

But obviously, I'm very concerned about what I found out. I want very badly to trust him but I just can't seem to let go of what happened (he still doesn't know that I know about the second time, and I dont want to tell him). My plan was to keep an eye on it, and keep snooping once in a while to make sure he was still behaving. If I find out he has done it again, I will confront him and probably leave him...
But in the mean time, how can I keep my silent distrust from ruining the relationship? I'm paranoid about it, but I want this to work, and I don't know what to do... I'm honestly not even angry about it anymore, I just want to know why. I want to know if it was just some meaningless moment, or if he really still has feelings for her...

[BackUpOrGetStng]

You can't keep silent distrust from ruining the relationship. You need to either let it go and stop snooping, or confront him and admit you snooped.

[Cerby]

Can you outline the "inappropriate" conversation? it might be a context thing.

[Alhaja]

it was written in a foreign language (my bf is here on a student visa) but I can read it quite well.. I did not read the entire convo, just the parts that jumped out at me as being suspicious, but the part i saw was this. They must have run into each other at a party when he went back to his home country to visit for a few weeks. She has had a steady boyfriend for a long time now.

She said "I'm sorry I had to leave so early," He said, "thats fine, its alright, your BF was there anyway. I wanted to kiss you so bad though, but i knew you wouldnt like it.... you should have seen me, my heart was beating so fast after" she said "mine too.... i have to get going though." he said "okay, well, maybe next year you will be single?" she said "I dont know, anything could happen, maybe I will be single" he said "I hope so :X "

after this they never talked again that I saw....