They exact numbers are unknown, but believed to be over 6000 Marines (six times above the limit).
It is said that only the High Marshal has any idea of the Black Templars' full numbers, but it is rumoured in the Inquisition that they actually number close to 6,000 Space Marines. That would make them nearly as large as some of the original First Founding Space Marine Legions after the terrible losses of the Horus Heresy, and means that the Black Templars are one of only three Chapters of Astartes (the others being the Space Wolves and the Grey Knights) thought to violate the 1,000 Space Marines to a Chapter limitation as proscribed by the Codex Astartes.
The Black Templars not as much ignore the Codex Astartes (as Space Wolves do), but rather found a loophole: in the Codex, each chapter was allowed to gather additional numbers, whenever they were participating in a crusade. Sigismund looked at that and declared, that Black Templars are ALWAYS on a crusade so they are following the law to the letter.
Lords of Terra and Inquisition are mostly fine with that, since the Templar forces are scattered across the galaxy.
Another possible contender (although you couldn't call it a chapter) is the
Unlike other Space Marines, the ones serving in the Deathwatch are not truly a separate Chapter of the Adeptus Astartes; rather, they are a collection of Veteran Space Marines drawn from all of the different extant Chapters who serve together in the Inquisition's service for a discrete period of time.
Their numbers are unknown and vary from time to time, but it is believed to be slightly below 5000.
Finally, similarly without exact known numbers is the
Similar to the Deathwatch, they are not a single chapter but a group of warbands of marines that abandoned their original chapter (or... legion!) and decided to seek redemption in the eyes of the Emperor. Originally Blackshield warbands were created after the Horus Heresy from the leftover loyalists from the Traitor legions. An individual Blackshield warband can count from few marines to well over 2000 and no one really knows, how many such warbands exist.