I'm not sure 'syllable' is the word your looking for. The definition of a syllable is "a unit of pronunciation having one vowel sound, with or without surrounding consonants" (Google). In Chinese each character corresponds to one syllable, and there is very limited set of syllables which is usually covered in the first few chapters of Chinese textbooks.

Actually, compared with many other languages the chinese cyllables are really quite limited. Think there are about 400 cyllables in total in mandarin chinese, with 4 possible tones in each. 

The problem for foreigners (at least for me) is that many of these sound quite similar, so it can from time to time be difficult to remember which word is which cyllable: zhang / zhan / zheng / zhen / chang / chan etc.. :)