To reassign the key globally, go to System Preferences » Mission Control and under Application Windows, where it currently says ^↓, assign another key (I used F10, à la exposé).
Firstly I am posting this as possible helpful info rather than a solution.
Which may get some one in the right direction.
I found this in the What's New in OSX which goes into explaining what and how Responsive Scrolling works.
At the bottom there is also a note saying how to disable it per app for testing purposes.
But I do not see this option in my own built apps or any others.
Responsive Scrolling
Responsive scrolling is an AppKit enhancement that makes scrolling
smoother. This involves two significant changes to the way your app
draws content:
Scroll views ask their child views to draw extra content outside their
normal view area so that the content can be immediately made available
for scrolling purposes. This additional window backing is stored in
purgeable memory to minimize additional paging. The scrolling thread
attempts to redraw the view at 60 frames per second, but it backs off
if the app is unable to keep up. Scrolling events are processed on a
background thread. Most apps automatically receive this responsive
scrolling behavior. However, some views must explicitly opt in,
including layer-backed views, custom scroll view or clip view
subclasses that override drawRect:, NSSurface-based document views,
transparent document views, and document views that override the
lockFocus method.
For views in which responsive scrolling is automatically enabled, the
behavior change should be entirely transparent to you as a developer.
However, if your app exhibits any unusual behavior while scrolling,
please file bugs.
Note: You can temporarily disable responsive scrolling for testing purposes by choosing File > Get Info on your app in Finder. After
changing the setting, you must quit and relaunch your app. For more
details, see AppKit Release Notes for OS X v10.9.
I had a look at the appkit release notes -Responsive Scrolling which goes into more detail.
There are conditions which should stop Responsive Scrolling being assigned to an App. One of them is:
The application links on 10.7 or prior (the application must link on
Mountain Lion or higher to support this feature)
Which I take to mean if the App is built to also run on 10.6 then it will not have this feature added.
Chrome AFAIK will run on 10.6 upwards. But I suspect the downloader is downloading a version for you current system.
Possibly a version built for 10.6 only would disable it in Chrome.
UPDATE*
But as bogdansrc points out in the comments. There is no single build for 10.6
I did try:
defaults write ~/Library/Preferences/com.google.Chrome isCompatibleWithResponsiveScrolling -bool NO
But the isCompatibleWithResponsiveScrolling is for a nsview sub class and I do not really expect it to work. I also am not getting this problem so I cannot tell.
Best Answer
If I might say so, why are you using the 3 keys to switch between the tabs.
In Chrome it is enough if you use two keys to switch tabs.
control + tab
If however you prefer to modify the the Chrome shortcuts, visit this website
https://chrome.google.com/webstore/detail/shortcut-manager/mgjjeipcdnnjhgodgjpfkffcejoljijf