Stand your ground on this one! Despite what the rest are saying, your spelling is perfectly acceptable. I would argue that it is SUPERIOR, and that the version without s, while admissible, is based on a mistake.
There are a number of respected usage manuals which regard "Chris's" as the correct, or at least preferred form. For example, here is the first part of a classic statement of the rule from Strunk & White's *Elements of Style*
1. Form the possessive singular of nouns by adding 's.
Follow this rule whatever the final consonant. Thus write,
Charles's friend
Burns's poems
the witch's malice
Exceptions are the possessives of ancient proper names ending in -es and -is, the possessive Jesus', and such forms as for conscience' sake, for righteousness' sake. But such forms as Moses' Laws, Isis' temple are commonly replaced by
the laws of Moses
the temple of Isis
http://www.orwell.ru/library/others/style/e/estyle_1.htm
The Modern Language Association and Chicago Manual of Style agree:
http://doesthisblogmakemybuttlookbig.com/2004/03/14/more-singular-proper-possessive/
I would take these over Microsoft Word any day of the week! (Do keep in mind that, in situations like this, spell-checkers tend to be set up to regard only one option as correct. As noted above, that ignores the option of allowing BOTH.)
I'll not go into detail here, but it seems fairly obvious that the notion that we ought to use simply "Chris'" (without the s) is based on a MIS-understanding. The rule about not adding an additional "s" applies almost exclusively to PLURAL forms ending in -s. But apparently some people never understood that detail and so began to apply it to singular forms ending in s as well.