Hard to answer this without having to dig into the history, which is somewhat confusing. The short answer is that there is an authoritative version of what is considered "Gregorian chant", but if you look at the history, the chant we know as "Gregorian" is a scholarly compilation of a particular chant tradition which ended up by taking precedence over other traditions. (The other traditions also survive in some form).
The Wikipedia article on Gregorian chant gives you the history, which shows different traditions arising in different places, and in time vying to be the definitive version. In the end what we now call "Gregorian" chant dominates over other traditions. This dominance seems to happen in two phases : the first phase ends in around 800 CE, when the emperor Charlemagne imposed on all his subjects a form of the Catholic service derived from the Roman one, which is the origin of Gregorian chant, and this was somehow also linked to the name of the Pope of the time, Pope Gregory - although there was no musical notation in use at that time to capture an authoritative version. The second phase is in the nineteenth century, when there was serious scholarly effort put in in the abbey of Solesmes, from about 1855 onwards, to reviving the tradition and compiling an an authoritative version. The Vatican commissioned the Benedictine Abbey of St. Pierre, Solesmes, France in 1904 to write the authoritative version, based on their previous work, although since that time there has been disagreement about the musicological accuracy of it. More detail on that in the wiki article.
The authoritative version is known as the Liber Usualis. Link is to a 1961 edition online, and since Gregorian chant is tightly coupled with the Roman Catholic forms of worship, the book gives all that context, in terms of particular chants for particular religious services or special days. 24 pages of the book are given over to "rules for interpretation", and the equivalents for traditional notation in standard musical notation, but the actual chants are in traditional notation. While this aims to be definitive, it is not very accessible if, like me, you are not familiar with the traditional notation. And the correct interpretation of the traditional notation is also subject of debate and disagreement as you will find from the references in the Wikipedia article.
If you want to follow this further, not sure what to suggest. There is a wealth of material on the subject online, and many sites devoted to teaching people to sing Gregorian chant.
Some random examples, which I hope will set you on your own journey of discovery with this:
Correction : taking into account comment from @Coemgenus on Charlemagne becoming Holy Roman Emperor and imposing Gregorian chant throughout his empire, date should be 800CE not 600CE as I originally wrote.
