The possessive of "Chris" is "Chris's."
You don't leave off the second S. With plural nouns you do leave off that S, like "the buses' route" (the route all the buses took), but I'm not sure why people want to leave off that S for singulars and names. It just looks amputated.
Here are some sources:
Perdue's Online Writing Lab
Strunk's Elements of Style
However, Capital Community College Foundation Guide to Grammar and Writing notes this:
Some writers will say that the -s after Charles' is not necessary and that adding only the apostrophe (Charles' car) will suffice to show possession. Consistency is the key here: if you choose not to add the -s after a noun that already ends in s, do so consistently throughout your text. William Strunk's Elements of Style recommends adding the 's. (In fact, oddly enough, it's Rule Number One in Strunk's "Elementary Rules of Usage.") You will find that some nouns, especially proper nouns, especially when there are other -s and -z sounds involved, turn into clumsy beasts when you add another s: "That's old Mrs. Chambers's estate." In that case, you're better off with "Mrs. Chambers' estate."
...most words that end in an unpronounced "s" form their possessive by adding an apostrophe + s. So we would write about "Illinois's next governor" and "Arkansas's former governor" and "the Marine Corps's policy." However, many non-English words that end with a silent "s" or "x" will form their possessives with only an apostrophe. So we would write "Alexander Dumas' first novel" and "this bordeaux' bouquet." According to the New York Public Library's Guide to Style and Usage, there are "certain expressions that end in s or the s sound that traditionally require an apostrophe only: for appearance' sake, for conscience' sake, for goodness' sake" (268). Incidentally, the NYPL Guide also suggests that when a word ends in a double s, we're better off writing its possessive with only an apostrophe: the boss' memo, the witness' statement. Many writers insist, however, that we actually hear an "es" sound attached to the possessive forms of these words, so an apostrophe -s is appropriate: boss's memo, witness's statement. If the look of the three s's in a row doesn't bother you, use that construction.
So yeah, people do leave off that S, sometimes for good stylistic reasons, and consistency is the key. But I'm going to take a completely useless and meaningless stand and say, if you don't have a stylistic reason, then please, Save the S.