Hawaii is self-sufficient in some vegetable and fruit crops but has become less self-sufficient in eggs, milk, livestock, hogs and pigs. In the 1970s, Hawaii was self-sufficient in eggs and milk with 240 eggs farms and 120 milk operations. Today there are about 100 egg farms and only two dairies. Livestock and hog and pig production have also declined since the 1970s.

About 85-90% of Hawaii’s food is imported

These quotes are from a Hawaii Department of Agriculture Report (pdf) compiled in 2012.

Before contact, Hawaii did face the occasional famine due to disease or not enough focus on sustaining their food source, and there is genuine risk today that outside forces (natural disasters, dockyard strikes, etc.) could create a serious food shortage. As of 2012, Hawaii has a ten day supply of perishables should disruptions to imports occur. There is also concern that environmental issues could increase Hawaii's reliance on imported food. (source) (word doc).

Hawaii faced the possibility of a food shortage in early 1942, thanks to the war. But at its worst there were only sporadic shortages of perishables, but by February of 1942, there was already a stockpile that would have been good for six months, should the worst happen. (source).

So, essentially: Since becoming a state it doesn't seem to have ever faced a serious food shortage. However, the state is incredibly reliant on the import of food, mostly from the United States, and there is concern within the state government that, should something disrupt imports, Hawaii could face a serious food shortage.

(worth noting: these figures are from 2012. The reality may have changed in the last five years, but it is the government, so probably not).

Edits to spelling/sourcing