How can I make Apple's keyboard shortcuts work in Chrome?
Chrome doesn't call Apple's spell checking code and instead wrote their own keyboard handling routines. Since this is how the program was made, there's not much of a workaround except to do your typing in a program that calls Apple's text input libraries and paste the results into Chrome. (Similar to how Dictionary lookup using Control-Command-D didn't work for several years on Chrome either until the code was updated to call Apple's SDK for that function).

You can see this Chromium bug might apply and also, that Chrome is in the process of removing it's own spell checker / autocorrect mechanism and shifting to rely on Apple's implementation: https://code.google.com/p/chromium/issues/list?q=label:Cr-UI-Browser-Spellcheck