You should be able to drag it on the desktop.(it will also stay in the menu)

Snake X are you using gnome 3 or cinnamon? I'm not sure how well gnome 3 supports launchers and I know cinnamon has them being developed. and did you install chrome or chromium? chromium is the version of chrome that most people use on linux(that I know of)

you should go with chromium instead. if you want what you have, though, then you can make a custom .desktop file.
just right click and make and empty file on your desktop, and then rename it chrome.desktop. then paste this inside it:
#!/usr/bin/env xdg-open
[Desktop Entry]
Version=1.0
Name=Google Chrome
# Only KDE 4 seems to use GenericName, so we reuse the KDE strings.
# From Ubuntu's language-pack-kde-XX-base packages, version 9.04-20090413.
GenericName=Web Browser
# Gnome and KDE 3 uses Comment.
Comment=Access the Internet
Exec=/opt/google/chrome/google-chrome %U
Terminal=false
Icon=google-chrome
Type=Application
Categories=Network;WebBrowser;
MimeType=text/html;text/xml;application/xhtml_xml;x-scheme-handler/http;x-scheme-handler/https;x-scheme-handler/ftp;
X-Ayatana-Desktop-Shortcuts=NewWindow;NewIncognito

[NewWindow Shortcut Group]
Name=New Window
Exec=/opt/google/chrome/google-chrome
TargetEnvironment=Unity

[NewIncognito Shortcut Group]
Name=New Incognito Window
Exec=/opt/google/chrome/google-chrome --incognito
TargetEnvironment=Unity