I have seen chirality being defined in a number of ways in terms of a molecule not being superimposable with its mirror image. My syllabus has a statement: "know that optical isomerism is a result of of chirality in molecules with a single chiral centre". This seems odd because surely you can have a have optical isomerism between molecules with more than 1 chiral centre so why a single. Overall, I am asking for either a confirmation that the statement is incorrect or an explanation of where my understanding is wrong.
I don't want to try to interpret the intent behind the wording of the phrase you quoted, so I'll just state the situation and you can read into it as you wish.
There is no truly general relationship between the number of chiral centres in a compound and whether it displays chirality overall.
However, if a compound has exactly one chiral centre, then it must be chiral. Compounds with more than one chiral centre may or may not be chiral, depending on what those chiral centres are and their relative stereochemical relationship. And as has already been rightly pointed out (4 seconds before me), compounds with zero chiral centres may still be chiral.
The statement is incorrect. You also don't even need a stereocenter (chiral center) to get chirality, as in the case of molecules with an axis of chirality.