A Google Ngram search of the Google Books database for the period 1800–2019 shows that chanterelle (red line) is much the preferred spelling today over chantarelle (blue line) and chantrelle (green line)—and has been for some time:
The preference for chanterelle is actually stronger in published writing than these line plots might suggest because many of the recent matches for chantarelle and chantrelle don't involve mushrooms at all, whereas the vast majority of matches for chanterelle do.
The dominance of chanterelle over the other two spellings (at least in U.S. English) is confirmed by the entries for chanterelle in both Merriam-Webster's Eleventh Collegiate Dictionary (2003) and The American Heritage Dictionary of the English Language, fifth edition (2010): neither dictionary lists any variant spelling for the word, suggesting that the lexicographers behind these dictionaries think that chantarelle and chantrelle have minimal followings today.
Correct spelling is ultimately a popularity contest, however, not matter of divine right. So if Whole Foods persists in its orthographical preference and manages to draw other influential publishers to its side, we may eventually see chanterelle/chantrelle go the way of catsup/ketchup.