What does Dimmesdale have on his chest in The Scarlett Letter?
It's an interesting question because the text is ambiguous about the answer. When Dimmesdale tears aside his shirt as he stands on the scaffold, supported by Hester, the narrator says, "It was revealed! But it were irreverent to describe that revelation." In this chapter, "The Revelation," then, the narrator doesn't describe what exactly "It" is that is revealed on Dimmesdale's chest because he considers it to be disrespectful to discuss it.
However, in the final chapter of the text, the narrator informs us that "Most of the spectators testified to having seen, on the breast of the unhappy minister, a SCARLET LETTER -- the very semblance of that worn by Hester Prynne -- imprinted on the flesh." This majority, however, disagrees about how the scarlet letter seems to have gotten there: perhaps the minister inflicted "a hideous torture on himself"; or perhaps it was the result of Chillingworth's evil, caused by "magic and poisonous drugs"; or maybe the letter simply appeared on Dimmesdale's skin as a result and symbol of "the effect of the ever-active tooth of remorse." The narrator does not know and cannot say. He says only that "The reader may choose among these theories" for him or herself.
Muddying the water further, though, is the fact that a few individuals who were present and claim never to have looked away from the dying minister in his final moments "denied that there was any mark whatever on his breast." Therefore, we cannot know for sure. It seems probable that a scarlet "A" did appear on Dimmesdale's chest, but we cannot be absolutely certain.
The common assumption is that he has some version of a letter "A" on his chest, although it is not clearly stated in the text. Different scholars have different theories on how the letter "A" could have gotten there -- did he burn or carve it himself? Is some sort of guilt-induced occurrence? In Chapter 12, Dimmesdale seems to have pain on his chest implying that that the wound is self-inflicted, but Hawthorne does not make it clear.
There are references to what is on his chest in Chapters 10 and 12.
Hawthornes gives several suggestions. One is that there is nothing there, and that his pain was spiritual not physical. Another is that he might have carved an "A" there during his self-punishment in the closet. A third is that some sort of rash or sore came up on his chest caused by the stress of his secret. It really does not matter, because the "A" was not the issue, the sin was.