At the time of the original post, the only way to make Chrome present decent looking images was to edit a command line in its Properties tab. That made it at least use the system monitor profile, which really helped wide gamut monitors. Unfortunately, whenever Chrome updated itself, which it did silently, the command line modification would be undone and ugly colors would return.
But now Chrome seems to automatically manage color quite well, especially when the images are "tagged" or "embedded" with a sRGB profile. And in the most recent versions it can even sometimes present un-tagged images nicely, which is something Firefox has done for years.
My current version of Chrome does not seem to exhibit periodic color management failures and recoveries, so I can only guess you are sometimes visiting sites that have un-tagged images, or perhaps Chrome is not automatically updating on your system, possibly due to security settings.
Chrome is a rapidly evolving work, with frequent silent updates. For the most part, those updates have been for the better.
FWIW if you save images for the web using PS's Save For Web, be sure to always check the "Embed Color Profile" box, and if you have not already done so, check the "Convert to sRGB" box.