Use
\chapter[TOC form]{text form}
at the start of each chapter. The TOC will have "TOC form" (supplied between square brackets) and the chapter itself will have "text form" (supplied between curly braces).
If the TOC form itself contains a closing square bracket (]), the
compiler will think the balanced brackets [] have ended and generate
an error. But rather than escaping the extra ], which may lead to
confusion with the math display environment, place the whole TOC form
within braces:
\chapter[{TOC form with closing bracket}]{text form}
I normally use the package titlesec for fine control of chapter
headings, but what is described above will work without it.
Remember that you have to compile your code twice in order to get the TOC to be updated correctly: once to typeset the whole text, and then once more to generate the TOC based on the typeset text.
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[Edited] for clarity.