You have always dreamed of your computer solving chess! Or your phone! The ultimate act of computation! Make a move! Sit back! Relax! Only the best for you! Very thorough! Very thoughtful! Good things take time!
Best Chess was written in JavaScript using the excellent libraries chess.js and chessboard.js, without which it would have been far too much work to bother with. The depth-first chess-solving algorithm is by Pippin (and is probably incredibly awkward and inefficient).
You can read writing about Best Chess on Pippin’s site. Best Chess has been written about on Kill Screen and Matajuegos.