Chardonnay is a bit of a pain to deal with. It can be VERY tempermental!
You do not say if you are making wine from a kit, pail juice, or whole grapes.
If you are making from whole grapes, then you are most likely pressing the grapes too hard and absorbing some of the more bitter tannins in the grape. I find that enven if I crush and destem the grapes, a lot of that bitter tannin come through.
To fight this, I took on a more labor intensive method of NOT crushing/destemming the grapes. Just toss the whole clusters into the press and simply press under light pressure over an extended period of time. I then allow the juice to cold soak for a day or two, then rack the juice into my primary. This removes any pesky seeds, skins, or pulp that is present in the must.
The results were well worth the effort. The chardonnay turned out crisp and very clean.