Today is the 2nd day of my periods and I had sex with my boyfriend without any protection.
Is there any chance of getting pregnant?
My menstruation cycle is of about 35-40 days

There is always a chance to get pregnant when you have sex. While on your period the chances are low, but still possible. Sperm can hang around for a long time, and if you're an early ovulator, then you could become pregnant. Again, the chances are low, but still present. I would use protection, a condom at least, at all times. A condom during your period because it cleaner for the male.

Good luck!

While the chance is very low, yes of course there is a chance.

If you have sex there is ALWAYS a chance of getting pregnant. You must ALWAYS use protect to to reduce those chances. No matter WHAT day of your cycle it is.