Does chemiosmosis require oxygen?

Hint: Chemiosmosis is defined as the movement of ions across a semipermeable membrane down their electrochemical gradient. The breakdown of this electrochemical gradient due to passage of ions leads to release (or you can say production) of energy.
An example of such a phenomenon will be production of ATP by passage of H+ ions from the lumen of thylakoids towards the outer stroma.

Complete answer:
We need to consider and understand how this process leads to generation of ATP in the thylakoids.
a) Since splitting up of water can only occur in the inner membrane of the thylakoid, thus the protons are only produced in the inner thylakoid membrane (in the lumen).

This oxygen acts as an electron acceptor in the ETS cycle and oxygen is released in the environment. Thus we can say that chemiosmosis indirectly releases oxygen.
b) This increases the number of protons inside the lumen of the thylakoids compared to the outer stroma region. This leads to the formation of an electrochemical gradient.
c) Thus, as the electrons move through the photosystems, protons are transported across the membrane. This phenomenon occurs since the primary acceptor of the electron that is located on the outer side of the membrane transfers its electrons not to an electron carrier, but to an H carrier.
d) Thus, as the protons get transferred, they pass through the transmembrane channel of the F₀ particle. The head (F₁) region of the particle contains ATPase enzyme. As the protons pass, ADP is catalysed by the ATPase enzyme that leads to the formation of ATP. 1 molecule of ATP is synthesized per 2 protons.

Note:
The point to be noted here is our concern and interest regarding the proton gradient. This gradient is important because it is because of the breakdown of this electrochemical gradient that leads to the release of energy or ATP formation. If this gradient fails to exist, then chemiosmosis will be absent, and no ATP will be produced.