Ahab is described as having a beard in Chapter 130: The Hat, though whether it's a "chin beard" or a full beard, etc. isn't specified.

Nor, at any time, by night or day could the mariners now step upon the deck, unless Ahab was before them.... [...]

He ate in the same open air; that is, his two only meals,—breakfast and dinner: supper he never touched; nor reaped his beard; which darkly grew all gnarled, as unearthed roots of trees blown over, which still grow idly on at naked base, though perished in the upper verdure.

That said, I'm not sure whether it's the case that he's "nearly always" portrayed with a chin beard. The most famous illustrated version of Moby-Dick, done by Rockwell Kent in 1930, does not give Ahab a beard. Patrick Stewart in the 1998 TV mini-series doesn't have a beard. William Hurt in the 2011 mini-series has a full beard, not a chin beard.

Gregory Peck's portrayal of Ahab in the 1956 movie with a chin beard probably has a lot to do with ingraining the physical image of the character in popular culture. But it actually seems to vary quite a bit.