1) Click on start and right click on "Computer" and click on "Manager".
2) Under your Computer management - got to Device manager.
3) Under device manager find "Keyboards" Expand it. Now right click on your "Keyboard device" and select Uninstall. Now right click again on Keyboards inside of computer management and select "Scan for hardware changes". This should re-load your keyboard laptop driver.
Also - typing lag can be sometimes caused by programs taking up a lot of CPU power - like games and such. Are you experiencing this type lag in general or while doing something specific?
Do you have an antivirus installed?
Is this a refurbished laptop, or brand new?
One more thing - you should try running windows update (even though its new, every month new patches are available) and then restart your computer once it's done.
Have you tried uninstalling - reinstalling your keyboard as per my suggestion above?
Also check this out when you have chrome open - right click on your taskbar in an empty space and click on Task manager. Now go to the "Processes" tab and see what happens when you type on any program, basically check the "CPU" column in the processes tab, if you see anything higher than say 20% for a certain running process there could be a problem.
Also do you have an antivirus installed? Sometimes viruses can cause such problems.