nonarchaeological

The story

1. Proto-Indo-European*né
2. Proto-Germanic*ne
3. Proto-Indo-European*ís?
4. Proto-Indo-European*h₁óynos
5. Proto-Germanic*ainaz
6. Proto-Germanic*nainaz
7. Proto-West Germanic*nain
8. Old Englishnān
9. Middle Englishnon
10. Old Englishnān
11. Old Englishnān-
12. Middle Englishnon-
13. Englishnon-
14. Proto-Indo-European*h₂er-der.?
15. Proto-Indo-European*h₂ergʰ-der.?
16. Ancient Greekἄρχω (árkhō)
17. Ancient Greekἀρχή (arkhḗ)
18. Ancient Greekἀρχαῖος (arkhaîos)
19. Proto-Indo-European*leǵ-
20. Proto-Indo-European*lóǵos
21. Proto-Hellenic*lógos
22. Ancient Greekλόγος (lógos)
23. Ancient Greekἀρχαιολογίᾱ (arkhaiologíā)
24. Englisharchaeology
25. Proto-Indo-European*h₂el-
26. Proto-Indo-European*h₂élisder.?
27. Englisharchaeological
28. English todaynonarchaeological

From non- + archaeological.