Chrome keeps creating Application folder in Home folder
Solution 1:
Google Chrome has a feature called App Launcher. If you install any apps from that part of the store the browser will put shims for the apps in ~/Applications (it also puts an identical copy in ~/Library/Application Support/Google/Chrome/Default/Web Applications/LONG_RANDOM_IDENTIFIER/). If it is doing this then you should have a folder within ~/Applications called "Chrome Apps". You can see the Chrome developers making the decision to use the ~/Applications folder here. If you have installed any Chrome Apps, just uninstall them and delete the "Chrome Apps" folder and then Chrome shouldn't recreate the folder.
If you are using Chrome Canary, by default it installs shims for Gmail, Google Drive, Google Search and YouTube. But if you delete the "Chrome Canary Apps" folder it doesn't appear to recreate it.
There are other applications that install to that folder though. On my own machine Steam has installed shims for games and GitHub has chosen to install there app there instead of /Applications for some reason (I may have been prompted, I don't recall).
Like Tetsujin said though, having an Applications folder within your own user account isn't really anything to worry about.
Solution 2:
I stumbled across this post while trying to get rid of what I see as annoying Chrome behavior. After fighting things for a while and trying different settings to prevent Chrome from adding its folder to my user folder, I decided to just hide it. It's a hack-y work-around, but doesn't offend my sensibilities. To do so, use the following command from the terminal:
chflags hidden ~/Applications/
Again, this just hides the folder so you don't see it. It's still there and still visible in the terminal.
Hope this helps a little :)