Is chess a solved game? Chess is a zero-sum game of limited decisions. The number of possible moves at any given point, and the number of possible states of the board, are all finite.

Tic-Tac-Toe, is one of the easiest examples of a solved game. I can't remember how many years it's been since I last lost a Tic-Tac-Toe match. Does any such "optimal strategy" exist for chess?

Is there any strategy that will guarantee the player would grasp victory or, at worst, a draw?

If there is, please shed some light on it.
Because of the observation you make, that the tree of possible game paths for chess is finite, chess is indeed solvable in exactly the same sense that tic-tac-toe is. So optimal strategies for chess do exist; however, no one has any idea what they are. Whereas tic-tac-toe is solved thanks to a quite small space of possible games, chess is nowhere near solved because its space of possible games far outstrips what could be dealt with by current computing technology.

As noted in another answer, endgame tablebases exhibit optimal play for all positions with limited numbers of pieces. So in those settings, we have solutions that are as explicit and concrete as are those for tic-tac-toe. But it's important to note that while one can easily teach/remember the optimal strategy for tic-tac-toe and swiftly become a perfect unassisted tic-tac-toe player, the amount of information behind, say, the 7-piece Lomonosov tablebases, is 140 terabytes. There is no concise description of optimal 7-man strategy that one could learn/remember and then play perfectly without assistance.