Thanks for filing the issue!

@Reporter: Could you please provide sample Test file/URL that reproduces the issue which helps us in further triaging it in better way.

Thanks!

https://jsbin.com/xiqihaf/edit?html,js,output

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The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/d32e99ba0badf7ce4becf9bd3873e600d22f087e

commit d32e99ba0badf7ce4becf9bd3873e600d22f087e
Author: Pavel Feldman <pfeldman@chromium.org>
Date: Tue Dec 04 19:33:35 2018

DevTools: exception message in the Paused on exception panel can't be copied

Bug:  879084 
Change-Id: I30e23daa5ed15cceca1e581249991a77fd3562e9
Reviewed-on: https://chromium-review.googlesource.com/c/1361646
Reviewed-by: Dmitry Gozman <dgozman@chromium.org>
Commit-Queue: Pavel Feldman <pfeldman@chromium.org>
Cr-Commit-Position: refs/heads/master@{#613644}
[modify] https://crrev.com/d32e99ba0badf7ce4becf9bd3873e600d22f087e/third_party/blink/renderer/devtools/front_end/sources/debuggerPausedMessage.css

Tested this issue on Windows 10 on the reported version 70.0.3536.0 and the latest M-73 73.0.3631.0 by following the below steps.

1. Launched Chrome and navigated to link provided in comment #3.
2. Opened Devtools -> Console and was able to select the exception message.
The same behavior is observed on the latest M-73 build

Attached is the screen cast for reference.

pfeldman@ Request you to check and confirm if anything is missed from our end in verifying the issue and help us to verify the fix on the latest M-73 build.

Thanks...

Deleted: 879084.mp4 1.3 MB

	879084.mp4 1.3 MB View Download

This bug is not about copying the message from console, it is about copying it from the debugger sidebar when execution is paused due to the exception.

1. open devtools
2. enable 'pause on exceptions' in debugger
3. in console throw new Error('foo');