I'm not new to color management, but this is baffling me. I selected the sRGB colorspace when exporting, so I would think it shouldn't matter whether or not the browser is color managed. And anyhow, both my MS Edge and Chrome browsers are color managed according to the test I ran here, but only Edge (and every other program I've tried that's not Chrome) is displaying it right. I'm running Windows 10 64 bit, with Chrome Version 56.0.2924.87 (64-bit).
I think it's something to do with the sRGB ICC profile embedded, and the way Chrome handles it. If I open the image in a photo editor (I used GIMP), select all and paste into a new file, export as JPG, then there is no ICC profile embedded, and it displays the same across the programs I tested.
See this comparison image--the color of the emeralds is less saturated in Chrome, and there's color banding to the left of the jewelry:
Is it a Chrome bug perhaps, or am I doing something wrong?
You need to understand that color management isn't one profile, but always two.
A single profile is just one hand clapping, so to speak.
Your monitor profile is the other half of this equation. The RGB numbers are converted from the document profile into the monitor profile, and these corrected numbers are sent to the monitor.
Applications without color management (those on the left) don't do this correction. They are wrong. They just pass the original numbers on, without correcting for your monitor's actual response (which is not accurate).
Browsers are a wild card. Most of them have some sort of color management, but bungled and inconsistently implemented. Don't use IE/Edge, and probably not Chrome. They don't properly convert into your monitor profile.
Use Firefox. It has the best and most reliable color management of all browsers.
Assuming that the FireFox browser shows it like Chrome does, my guess would be that the programs that show the image as more saturated are not applying your monitor profile to the corrected color space. Microsoft viewers are well known for not getting this right.
When LR shows the image, which version does it look like?