First of all, thanks for all your comments. Most people seemed to like Chess' better than Chess's, but through a little research, I think I am going to start using Chess's for two reasons.
1. Although both ways are correct, I found this semi-rule:
A singular noun ending in "s" takes either an apostrophe or the full 's depending on whether we pronounce the word with an added syllable or not.
For example, we say Chris-es house (Chris's house). We pronounce the extra syllable, so we write the full 's.
But, we say Achilles- heel (Achilles' heel). We do not pronounce the extra syllable, so we write only an apostrophe.
2. I saw this book cover:
I love Dr. Seuss, and if a triple S isn't too crazy for him, then it's not too crazy for me.
Since before Chess was born, I anticipated a problem using the possessive form of her name. I'm pretty sure the rule allows you to choose whether or not to add only an apostrophe, or an apostrophe and an s to make a singular noun ending in s possessive.
I have been using "Chess' toys" (for example) because her name ends in a double s making "Chess's toys" if I did it the other way and that looks a little crazy to me. But I am starting to rethink it because it looks like you should pronounce it just "Chess" instead of "Chess-es."
So what do you think? Chess' or Chess's