Even by conservative estimates, there are probably dozens of people in DC continuity who know Batman's secret identity. Today we check on someone who at least thinks she's on that list: from 1998, Chase #8, "Shadowing the Bat, part two: Truths" Co-plot and script by D.Curtis Johnson, co-plot and pencils by J.H. Williams III, inks by Mick Gray.
The Department of Extranormal Operations' Mr. Bones sets up the premise for this one: the shadowy government agency is going to have Agent Chase test a theory. They know Batman is real, and want to use her as a snare to expose his real identity. (Bones's explanation makes it seem like the DEO could expose a great deal about Batman, but can't or won't do so without the name to hang it on.) Having little love for caped types, Chase is more than up for it, and takes a drug case in Gotham: it's a legit case, but a better cover.
Chase does take care of the drug case, working with Detective Bullock; and stays an extra day to attend a charity party hosted by Bruce Wayne. This was post
Alan Scott, whom Chase immediately pegs as "veteran mask," especially in contrast to a couple of "schmoozers" like Bruce Wayne and Dick Grayson. Scott even makes a lame excuse about having to leave early, which is just more fuel for her fire. She tries to trail Batman outside of GBC later, but is surprised by the Dark Knight; who confronts her with ballistics evidence from her drug case, suggesting her partner may have murdered a dealer. Oh, and revenging yourself on superheroes won't bring your dad back, 'kay, bye.
Pissed, Chase gives, um, chase; intent on confronting Batman. Chasing him through a condemned area of town, she acknowledges the danger of buildings "too damaged to use, too intact to easily demolish," right as Batman takes a nasty fall off of one. Stunned and helpless, Batman couldn't possibly stop Chase from unmasking him--if she wanted to. Instead, she tells him she doesn't do her job for revenge, but so no one else has to go through what she did. She tells Batman his secret is safe with her, and walks off...
...as Nightwing and Batman help the fallen Dark Knight, a disguised Alan Scott! The former Green Lantern, now Sentinel, wonders what that was all about: they had planned to confuse the issue, and throw Chase off all of their secret identities, but no need now. Which is good, since she probably would've considered it a dick move, and exposed them all to get 'em back.