Congratulations, that's so exciting! Which race are you training for?
I really hate to give an answer like this but: it just depends! For myself, it seems around 8-ish miles or longer is entering potential chafe territory. So, you might be getting close with the distances you're running. But it also depends on the weather and the sensitivity of your skin. The more sweaty the run, the higher the likelihood of chafe. Cooler weather is here (at least where I live!) so that could keep you from getting it at all.
Something you could do is just get a travel-sized container and keep it handy. If you start feeling a sting, but aren't done with your run, apply as necessary and it should help keep it from getting worse.
Good luck with your training, I'm so excited for you!