In the uploader in Chat, when putting an image on Stack Imgur from the web, it doesn't make the link it puts in the message use HTTPS. Here is an example of the uploader doing this. This should be changed to make the site more secure.
When editing the message, you can see that the link it makes to the image is not secure:
https://i.sstatic.net/EFhdU.png
Very minor, but, if we had Community changing every single link to Stack Exchange to HTTPS, it seems good to make Chat use HTTPS links with the uploader.
https://i.sstatic.net/EFhdU.png
as it should be. (In the example you gave) If you see something else, it's on your end, something is messing with your web pages, check for viruses and malware.