Tested this issue on chrome reported version 66.0.3329.1 using Mac 10.13.1 with steps mentioned below:
1) Navigated to System Preferences -> Accessibility -> Mouse and Trackpad -> Trackpad options and selected three finger drag in Enable dragging dropdown
2) Launched chrome reported version and navigated to Google.com and apple.com
3) Swiped to left with three fingers, page didn't get navigated to previous visited site

Tested the behaviour on 65.0.3322.3 as mentioned in comment#0, even seeing the same behaviour when swiped with three fingers i.e., page didn't get navigated to previous visited site. But when swiped left and right with two fingers page get navigated as excepted.

@Reporter:
Please find the attached screencast for your reference and let us know if we missed anything in reproducing the issue, provide your inputs on it for further triaging it in better way.

Thanks!

Deleted: 805241.mp4 2.3 MB

	805241.mp4 2.3 MB View Download

Sorry, it's not the three finger drag under Accessibility. It's under System Preferences -> Trackpad -> More Gestures -> Swipe between pages and select the Swipe with three fingers from the dropdown

Thank you for providing more feedback. Adding requester "sc00335628@techmahindra.com" to the cc list and removing "Needs-Feedback" label.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

I can confirm this. I think it showed up within the last few days, so I'm going to tentatively mark it M-56. Needs a bisect.

Able to reproduce the issue on reported version 66.0.3329.1 and latest version 66.0.3330.0 using Mac 10.13.1 hence providing Bisect Info
This issue is not specific to Ubuntu 14.04 and Windows-10
Bisect Info:
================
Good build: 66.0.3328.0
Bad build: 66.0.3329.0

You are probably looking for a change made after 530906 (known good), but no later than 530907 (first known bad).

https://chromium.googlesource.com/chromium/src/+log/44cf3977560cac12416f8f88a93aa92628cf0e57..dec06ed3705dc353977df4441eed7cb16d170927

Reviewed-on: https://chromium-review.googlesource.com/852978

@Jayson Adams: Please confirm the issue and help in re-assigning if it is not related to your change.

Thanks!

The issue is when the BWC was the NSWindowController/delegate it was in the responder chain and so received swipeWithEvent:. Now that its no longer part of the responder chain this message does not get handled.

rsesek@ - do you think I should make TWC inherit from NSResponder and stick it in the responder chain, or manually forward these messages along (I'm unsure if there are others).

I don't have a strong preference either way. Adding it as an NSResponder seems marginally better, though?

It's better because it's cleaner (in this instance TWC has to know about a method that BWC implements) and less fragile (there won't be a question of why the responder method swipeWithEvent: works but not others if you try to add them). I just get a little nervous about mucking with the responder chain. But, I have taken the responder chain approach and have posted the cl.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/d4110a686aebf40bdc14ebbbc80626bd00aaa19a

commit d4110a686aebf40bdc14ebbbc80626bd00aaa19a
Author: Jayson Adams <shrike@chromium.org>
Date: Mon Jan 29 17:05:48 2018

[Mac] Fix three-finger swipe breakage by adding TWC to responder chain.

The recent change to separate TabWindowController from
NSWindowController also removed it from the responder chain. As a result
messages like swipeWithEvent: no longer reached the
BrowserWindowController BWC. This cl reinserts the TabWindowController
into the responder chain, before the window's NSWindowController.

Bug:  805241 
Change-Id: Ifa46d3e66ad306f26d860fe196f445e76fe293a4
Reviewed-on: https://chromium-review.googlesource.com/887326
Commit-Queue: Jayson Adams <shrike@chromium.org>
Reviewed-by: Robert Sesek <rsesek@chromium.org>
Cr-Commit-Position: refs/heads/master@{#532466}
[modify] https://crrev.com/d4110a686aebf40bdc14ebbbc80626bd00aaa19a/chrome/browser/ui/cocoa/tabs/tab_window_controller.h
[modify] https://crrev.com/d4110a686aebf40bdc14ebbbc80626bd00aaa19a/chrome/browser/ui/cocoa/tabs/tab_window_controller.mm

Verified the fix on Mac 10.13.1 Chrome version #66.0.3335.0 as per the comment# 14
Attaching screen cast for reference.
Observed "Able to swipe back and forward using three fingers"
Hence, the fix is working as expected.
Adding the verified label.

Thanks!

Deleted: 805241.mp4 930 KB

	805241.mp4 930 KB View Download

Indeed it is working. Cheers!