Not so many years ago, supermarkets were a rare breed in Crete. They have now sprung up all over the place in all the cities. Out of the cities you still need to rely on smaller shops, but they too are growing in size.
At present there are three main chains of supermarkets in West Crete:
Until recently named INKA they were probably the first supermarkets in the Chania district. When possible they offer products of local origin.
Less common, Halkiadakis (Spar) offers more or less the same range as the two above as well as some of their own brand products.
AB (Άλφα-Βήτα Βασιλόπουλος) is a relative newcomer in Crete. Good range of products as well as own brand.
The German discounter Lidl also entered the Greek d Cretan market in the early 2000s and expanded rapidly (Lidl now has 4 shops in the Chania region).
Apart from these big ones, there are a number of single place supermarkets, large and small. There are also many smaller supermarkets in tourist areas (especially on the North coast west of Chania) operating during the tourist season. These last are a little more expensive, but only a little. They often keep longer hours and may be open on Sunday.
You can find almost anything you need in supermarkets although the availability of foreign products varies quite a lot. Most of the foreign products not used by the Cretans can be a lot more expensive than in their countries of origin.