Yes, NEOLITHIC is a Scrabble word!

Letter values in Scrabble US: N 1, E 1, O 1, L 1, I 1, T 1, H 4, I 1, C 3.

Is it a valid word?

NEOLITHIC is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

latest part of the Stone Age beginning about 10,000 BC in the Middle East (but later elsewhere)

of or relating to the most recent period of the Stone Age (following the mesolithic)

Also: neolithic age, new stone age.