I use Chrome on Windows8 laptop, with the IE-Tab addon. This works fine and allows Chrome to be used to access ByDesign. Sofar I haven't experienced problems. Only drawback is that IE-Tab adds a second address bar in which you type your https://myXXXXXX.sapbydesign.com url.
REcently I tested a Chromebook too. In its native Chrome browser, I added from Google Webstore the tryout version of the addon IE-On-Chrome. Although I didn't do extensive testing it seems to work nicely.