Do you have to refrigerate Pickles?
Traditional fermented pickles were kept in barrels, but they're not the kind that you buy in a big jar at Costco. Those pickles have been briefly cooked in a brine, and should be refrigerated after you open the jar. The salt and vinegar should keep them safe for a while, but they will likely go bad at room temperature before you finish eating the whole jar.

As an anecdotal note, an office I used to work in kept one of these large jars of pickles around. After being open for a few years, they were clearly spoiled, and nobody would touch them.