Who has the "tell-tale" heart in the story: the narrator or the old man? Defend your choice.

The "tell-tale heart" in Poe's short story most definitely belongs to the narrator.  

The narrator thinks that he has an "over-acuteness of the sense[s]" because he believes that he can hear the old man's heart; however, it is really his own heart that he hears. On the night he finally kills the old man, he accidentally wakes him up first, and after waiting an hour for him to lie back down, the narrator opens...

The "tell-tale heart" in Poe's short story most definitely belongs to the narrator.  

The narrator thinks that he has an "over-acuteness of the sense[s]" because he believes that he can hear the old man's heart; however, it is really his own heart that he hears. On the night he finally kills the old man, he accidentally wakes him up first, and after waiting an hour for him to lie back down, the narrator opens his lantern just a bit, and the light falls on the man's "vulture eye"; the narrator "grew furious as [he] gazed upon it." When we get angry or nervous, adrenaline is released, and our hearts begin to beat faster and more loudly. At this point, the narrator says, 

[...] there came to my ears a low, dull, quick sound, such as a watch makes when enveloped in cotton. I knew that sound well, too. It was the beating of the old man's heart. It increased my fury, as the beating of a drum stimulates the soldier into courage.

There is simply no way that the narrator would be able to hear the old man's heartbeat from across the room. It is only logical to assume that the heartbeat he hears is his own, beating harder and faster because of his growing "fury."  

Furthermore, the narrator hears this same sound even after he has killed and dismembered the old man. There is, again, simply no way that the sound could be coming from someone who has been murdered and cut apart. While the police officers sit just on top of the spot where the narrator buried his victim, he again hears

a low, dull, quick sound -- much such a sound as a watch makes when enveloped in cotton. [He] gasped for breath -- and yet the officers heard it not.

The narrator is growing more and more nervous that the officers will find him out (he says "[his] head ached, and [he] fancied a ringing in [his] ears"), and so his heart begins to beat loudly and more quickly once again. He describes the sound in precisely the same way as before -- a watch wrapped in cotton -- and as he gasps for breath, the sound will only increase like it did before. Further, the officers cannot hear it, and so we must assume that it is actually the narrator's own heart that he hears.