The chemistry requirements are minimal. You should understand the difference between ionic and covalent bonds, how van der Waals forces work, hydrophobicity, solubility, and the effects of catalysts on reaction transition states. It will also be important to understand what reaction kinetics are and what pH means. An understanding of buffers might be useful.

I would argue that, to understand the book, you specifically don't need to know electrochemistry, organic chemistry, analytical chemistry, organometallics, spectroscopy, or even physical chemistry.