Yes, they use TEA-TEB (Triethylaluminum-Triethylborane) as their first stage ignitor and this mixture is hypergolicpyrophoric (i.e. hypergolic in contact with oxygen, be it atmospheric or LOX), but no, they don't ignite one engine and let that one ignite all the others, they would want to ignite them all at once. Problem with one engine igniting others is that doing so would create a pressure spike that would likely damage the engine and, according to Ben Brockert, CEO of Able Space Co., Denver:
The fire would then travel up into the engine where it would create a massive pressure spike, definitely destroying the engine and possibly destroying engines nearby. In propulsion testing the euphemism for this is a "hard start" leading to "rapid unplanned disassembly".
Quote source and more information via Joseph Abbott's Joe Science blog post: The TEA-TEB glitch: Can't light a Falcon 9 without a spark