We study one-sided partial-information 2-player concurrent stochastic games with parity objectives. In such a game, one of the players has only partial visibility of the state of the game, while the other player has complete knowledge. In general, such games are known to be undecidable, even for the case of a single player (POMDP). These undecidability results depend crucially on player strategies that exploit an infinite amount of memory. However, in many applications of games, one is usually more interested in finding a finitememory strategy. We consider the problem of whether the player with partial information has a finite-memory winning strategy when the player with complete information is allowed to use an arbitrary amount of memory. We show that this problem is decidable.