Yes there is a chance on getting pregnant .A.N.Y.T.I.M.E you have sex, protected or not, period or not.

Not sure exactly when i conceived but we began having sex while i was still on my period and i ended up pregnant a short time later.. I think it is fully possible.

possible - yes.
probable - no.

you see, ovulation typically occurs 14 days before your next period is due.
let's assume a typical 28 day cycle and therefore ovulation being likely around day 14 (day 1 being the first day of bleeding).

this places your window of highest fertility between days 9 thru 15.

however, it is quite possible that you ovulate early or late.
as it is not possible for us to know this we can not say for sure if *you* could get pregnant on your period or not.

I can say for 100% though that yes it is possible but not it is not probable.

either way you should use condoms as they protect against not only pregnancy but diseases too.
and as your cervix is slightly open during yout period and your tiny blood vessels are also open (hence you bleed as the uterus lining comes away) then you are at a greater risk of infection.