If drinking Chalk Hill Estate Chardonnay as an aperitif, it would do very well alongside a charcuterie board and a selection of cheeses (ranging from mild to super funk).
For a main, we would recommend a soft, smooth-textured, and mild seafood like seared scallops, halibut or even sea bass. Serve it against something acidic — like a micro-green salad dressed with a kicky vinaigrette and garnished with a few raw nuts — to elevate the overall acidity on the palate (since the acid in the wine is so low).