The Swiss statement
Swiss HIV experts have said that an HIV positive partner on treatment with an 'undetectable' viral load for at least six months won't pass on the virus during unprotected sex - so long as it is within a monogamous relationship free of STIs. This has become known as 'the Swiss statement'. If an STI enters the relationship from outside it will make the viral load of the HIV positive partner go up, increasing the risk that HIV is passed on.
However, other experts do not agree with the Swiss statement because there are cases of people with undetectable viral load infecting others, including inside monogamous STI-free relationships.
You should both get advice from an HIV specialist before making any decision about not using condoms.