@bgeiselman :-
Welcome to the "kennels". Nice to have you here.
There have always been ways to run Chrome as the 'root' user, though as others have said, this is NOT the Google-preferred way! Running the majority of apps as the root user is perfectly safe in Puppy.....why SHOULD you have to run a single-user system in the same way as a multi-user one, i.e, asking your system's permission to do every little thing? However, for anything internet-facing (like browsers) I find it preferable to follow accepted practice and run them AS the Puppy restricted-user "spot".
Way back around 2016-17, we found that Google had moved the goalposts, and begun to insist on running their browser as a restricted user.....at that time, the usual Puppy hacks had quit working. So, we found the only way around this was to start adding the 'home' directory to the root "/" file-system, in order to emulate the mainstream layout of /home/user.....where everything runs as a restricted user.
(Since then, other ways to achieve the original Puppy run-as-root Chrome have been found, like the "--test-type" 'wrapper' exec-line "switch", although this is intended, by Google, primarily for developers.)
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A year or two later, we began developing the Puppy-portable system. One of our devs - @fredx181 - figured out a way to do this with Firefox. I was intrigued, since I'd always wanted to do this with Chrome itself, in the same way as the Windows PortableApps. Mucho experimentation followed, and it wasn't long before I'd sussed-out & understood the nut's'n'bolts of the process.....after which, there was no stopping me, and shortly after - with plenty of assistance from other community members! - we had a whole range of 'portable' browsers.
Having evolved the 'home' user method for the Chrome SFS packages a couple of years earlier (thanks to @jamesbond), I turned my attention to the best way of implementing this for portable-Chrome. Turned out the way to achieve it was to create a mini-"spot" directory within the portable itself (with appropriate permissions), then create profiles, etc, inside that. Downloads will end up in the /home/spot directory - this is now standard across all Puppies - but in every other respect, the portable Chrome is self-contained, and can be run in literally ANY Puppy.......either from a flash-drive, or from outside Puppy itself, and then 'linked' into any Puppy you wish to use it in. This way, a single instance of the browser can be shared between several Pups......and it removes the need to have to 'sync' your profile with Google's servers, too, since all Puppies are using the same browser AND profile.
After this, since many of our members are concerned about internet security, I began to add the ability to some of the other 'portable' browsers for the user to choose, at launch time, whether to run-as-root OR run-as-spot (Iron, Slimjet & Opera ATM). And since the built-in Chrome update mechanism doesn't function in Linux the way it does for the Windows build, I subsequently figured out a 'manual' method to do THIS via a script (after much head-scratching!).....which Fred later developed into a fully-automatic mechanism that checked for updates every time you fired it up. It works rather well!
Anyways, enough of this waffle. If you're interested, the 'other' portable-Chrome can be found here:-
viewtopic.php?t=146
Entirely up to you, of course. Like everywhere else in Linux, there's lots of ways of achieving the same result.....and although shinobar's portable Chrome & my portable Chrome go about it in different ways, the net result is the same. We all bounce stuff off each other, and borrow ideas & concepts here and there as needed. It's what a community is all about; at the end of the day, we just want to try and improve the Puppy experience for everyone.
(The main reason mine is back on page two of "Browsers & Internet" is simple.......because once you've downloaded it, it keeps itself up to date. You don't need to keep re-visiting the thread to download a new version.....(*shrug*)) 
Mike. 
to the forums!
