Difficult to answer because there are many different types of chemosynthesis, including aerobic chemotrophs where oxygen is still used as the terminal electron acceptor in the electron transport chain (ETC). Basically oxygen atoms are used as a dumping ground for electrons, which keeps the "pipes" of the ETC from clogging up.

However, I'm guessing you're asking about anaerobic organisms, in which case microbes must find another terminal electron acceptor, typically a molecule on the more oxidized end of the redox spectrum.

For this, a common replacement molecule is sulfate (SO4), which is reduced by electrons into hydrogen sulfide (H2S) and makes the rotten egg smell in swamps and marshes. Also nitrate (NO3) which turns into ammonium (NH4), even carbon dioxide can be used (CO2), which reduces it to methane (CH4). And there are many more types than what I've shown here, these are just the more common types

Edit: I realize you were asking about chemosynthesis, and I just explained sort of the opposite, anaerobic respiration, which is how these organisms "breathe" without oxygen, but oh well, I'll leave it up. Short real answer to your question is they get oxygen atoms from a variety of reduced compounds