Okay, that's good to know, thanks guys! It must be the result of an addon / extension that's acting up for some reason. I'll go and do some tests.

2 seconds later:
Click image for larger version. 

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(Random image of the South Atlantic Anomaly)

Huzzah! Turns out I had an extension called uBlock (a free ad blocker that was automatically installed on Chromium that one time I messed around with Linux... and somehow got transferred to Chrome once I logged into Chromium with my Chrome account). I never minded that it was there, but it never did anything for me either... so I just deactivated it, an lo and behold, I can add images again!

Thanks for your suggestions people, and for confirming that it had to be something on my side, and not at Chrome or Cartographersguild.com. Phew!