Problem solved: Why doesn't Chrome remember its window size settings?

Position of the window is only saved if the state (maximized/minimized/restored) is changed.
So, move the window to where you want it, then size it a little (this can be done before the move), and then shut down Chrome and restart. This is still really a bug, but at least there is an easy work around. 
Note: in fact, needn't to restart the Chrome.