Being chary (pronounced CHAIR-ee) is being wary or cautious. Chary is the word "char" with an added "y" and to char is to burn, so if you're careful and don’t want to get burned by a person or situation, you're chary.
If you "test the waters" before diving into a situation or relationship, you're being chary. When something looks too good to be true or someone is selling something a little too eagerly, you might want to take a step back, being chary about any steps forward. A synonym of chary is "wary," and both include caution, but some definitions suggest that it's obvious when someone is wary — it shows — while being chary is more of an inside, or hidden, distrust.