I have 2 chimneys, a Weber and some other brand. The other brand doesn't light well, and that oil on the paper trick works great. The Weber chimney requires 2 sheets of crumbled up paper and starts almost every time without any oil or addition re-lighting.
Er, uh, at least, withe Kingsford it does. Lump charcoal, on the other hand, has so many odd-shaped pieces, they don't fit in the chimney as well as the briquettes, and I find it harder to light as a result. Using oil on the paper can help.