I know the popular theory is that Tommy Merlyn is Prometheus and while that would be awesome it seems unlikley as he's been dead for years now, and his actor Colin Donnell is full time on Chicago Med at the moment. So within the realm of what's been established I believe D.A. Adrian Chase is actually Prometheus. Yes Adrian is tradtionally Vigilante in the comics and while I am convinced he is stillI, just don't trust him and I know think he's both individuals. After all this wouldn't be the first time a well known character has taken on the identity of two well known superheroes/villains.
According to Felicity the weapons Prometheus uses are all fashioned from Oliver's discarded arrows over the past 5 years which only S.C.P.D. would have access to via the evidence locker, which implied him to be a police officer. However Adrian is the D.A. so he would also have access to the evidence locker. Adrian also became D.A. right around the time Prometheus showed up. He could have been climbing through the systems as a lawyer and now as D.A. for the last 4 years specifically to gain access to Oliver's arrows and forge his weapons with them, as part of his plan for revenge.
Prometheus is also speculated to be the son of Justin Clayborne and while I originally thought this may have just been a msidirect what if it's not? Clayborne's son according to Felicity based on his son's baby photo would be about 30 years old today, which is about Adrian's age and as his son is illigitimate he won't share the same surname. Yes Clayborne was a dirtbag and criminal, but people can be blinded when it come to family and Clayborne could have loved his son dearly despite the monster he was. To this end Adrian could have been devastated when he lost his father and swore revenge on "The Hood", even if it meant killing people himself because as Rory pointed out, the message of Prometheus' killings is his belief that Oliver is the serial killer which, lets' face it, crossing names off a list is boarderline
I am also convnced Prometheus has a connection to Talia al Ghul and I'm actually starting to think that she, not he, is the true main antagonist of this season, though of course Prometheus is still not to taken lightly if this is the case. Adrian shouldn't have any knowledge of time travel or multiverse but Talia is League of Assassins and they existed for thousands of years, and they pretty much know everything. For more hard evidence Talia knew Sara Lance between 1958 and 1960 during her time marooned and even if Ra's didn't tell her Sara was a time traveler, chances are she discovered it for herself while researching Oliver in 2012. And if she does have a grudge against Oliver for whatever reason she may have been keeping tabs on him which could have included Barry, and could have learned of the Multiverse as they were frequently exploting it last year. As for the Waverider, similiar reason as before, she could have been keeping tabs on Sara too and the Waverider has made several trips between 2016/2017 Star City. The Waverider has also made a few trips between 1960 and 2016, including 1975, 1986, 1990, 2007, 2014 and 1967, so it could have been documented by a bystander and in turn found it's way to Talia.
So if Talia is the true mastermind behind this years' plot as I think she is she could have found a vengeful Adrian and trained him in all the ways she taught Oliver, as a means to taunt him by creating a dark version of what Oliver could have potentially become, and as a major misdirect so when Oliver finally defeats Prometheus, Talia herself makes her move. Again this doesn't mean we don't take Prometheus seriously as a villain as he's still done a lot of horrible things this year, and Talia or no Talia will have his own reasons for wanting Oliver dead.
Now as for Vigilante. I'm not as clear on how he fits but I am just as sure that Adrian Chase is Vigilante as I am convinced he is Prometheus. Prometheus actually seems to be based on the new Batman character Arkham Knight who after his identity was revealed reformed and became the Red Hood, a vigilante not afraid to use guns or kill people to see justice done. Maybe Adrian is using his "Prometheus" persona as a means to an end to get his revenge on Oliver by taking everything from him, then by taking up his "Vigilante" persona full time as the new defender of Star City and believe he'll be a better defender than Oliver was. Or Vigilante is simply a misdirect identity to make Oliver think he's hunting two individuals who are both threats for very different reasons, but are actually the same person. Also the comic Prometheus' real name is unknown so it literally could be anybody and I'm stil convinced Adrian is Vigilante so they could just as easily merge the two identities.
Just speculation but I don't trust Adrian and he, Prometheus and Vigilante never seem to be in the same episode together and when there are, Adrian isn't usually in it for every long before Prometheus or Vigilante appears.