If I play an ally during the combat phase using the event "Sneak Attack," do I still pay the ally's cost (with appropriate resource tokens) in addition to the 1 [leadership] token for the Sneak Attack event card?

Sneak Attack: "Put 1 ally card into play from your hand..." Does "Put into play" allow me to deploy the ally without paying its cost? As opposed to, "Play 1 ally from your hand"? Am I overanalyzing the grammar of the Sneak Attack card?

You put it into play from your hand. you do not pay the cost.

Elven Archer said:

You're not overanalyzing at all. In fact, you've hit on a key grammar distinction (the difference between "play" and "put into play") that is common to all the FFG LCGs.