That's strange because I can place unnumbered and encore chapter markers at every frame, also snapping can be disabled by clicking on the icon in the timelinewindow.
Maybe you can post a printscreen of your timeline so it's easier to see what's going on?

If you don't manage to solve it I think the only thing you can do is to reinstall premiere and right after that update to version 3.0.1 (374)

I am able to place Clip Marker on ANY exact frame in CS3, even with Snapping on and zoomed to full sequence. It's best to navigate by Cursor keys Left and Right - this jumps between single frames.

Thanks for the help guys. I have uploaded a jpeg of the timeline. As you can see it's zoomed all the way in and as Yossi mentioned, it's snapping to the nearest fame. The project is in 24p (music video) and I am trying to line up the audio track with the exact same audio queue that was on the video shoot. They are off by like 1/2 a frame as you can see. is there any way around this do you know?

Ok, this is clearer, this is how it should work; In the timeline window menu (in the right upper corner, very small arrow) select "audio units" and turn off "snapping" on the time line (you can toggle that using "s" on the keyboard)
The timeruler now counts the audio samples instead of videoframes.
Zoom in completely again and you will see that you can drag the audio clip much more accurately.
To change the timeruler back to videoframes again just deselect "audio units" in the time line window menu.

Noa ~ This is precisely what I was looking for. THANK YOU - I have been trying to find an answer to this all night :) - you saved me a lot of trouble, thanks so much ! Also to the others that posted - changing the timeline to show "Audio Time Units" via the arrow on the right worked like a charm and now I can easily move the audio to the correct placement in the track! - Now I can actually start editing this video :)

Glad that I could help, I have the "premiere pro for windows book" from Antony Bolante which is basicly for version 1.5 but has been a great help for me when I started using premiere. I got mine from a large booksale in Antwerp for only 9 euro which was a bargain. I still use it, even now with premiere cs3.
I'd really reccomend this book as it's easy to read and shows you all the tricks possible, there is an updated version now. http://www.amazon.com/Premiere-Pro-C.../dp/032152635X

Thats really great information, I will look for the book - thanks again for sharing your knowledge it's really appreciated!