Yes, STILLEST is a Scrabble word!

Letter values in Scrabble US: S 1, T 1, I 1, L 1, L 1, E 1, S 1, T 1.

Is it a valid word?

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

not in physical motion
marked by absence of sound
(of a body of water) free from disturbance by heavy waves
used of pictures; of a single or static photograph not presented so as to create the illusion of motion; or representing objects not capable of motion
not sparkling
free from noticeable current

Not playable in Scrabble US: NONEFFERVESCENT.