Nope, no such thing as an atheist chaplain, minister, priest, Agga, Lama, preacher, pastor, Imam, Rabbi...
Of course not but that's never been a problem to the military. When i did my basic training (Australian army) we were given two choices: Volunteers for church parade form up on the right, volunteers to carry rocks form up on the left. We all went left. Instant conversion.
Donating blood was done the same way. Volunteers to donate blood form up on the right.... (as I recall, only one man offered to carry rocks, and they worked him all day.)
No ... Because it IS oxymoronic.
Military chaplains can perform services for many faiths ... But atheists are not a faith.
They SHOULD employ "Counselors" for that particular position . . Not Chaplains.
Someone you can talk to, to help in guidance mental stability.