We present spectroscopic and photometric observations of the Type IIn supernova (SN) 2008iy. SN 2008iy showed an unprecedentedly long rise time of ~400 days, making it the first SN to take significantly longer than 100 days to reach peak optical luminosity. The peak absolute magnitude of SN 2008iy was M_r ~ -19.1 mag, and the total radiated energy over the first ~700 days was ~2 x 10^50 erg. Spectroscopically, SN 2008iy is very similar to the Type IIn SN 1988Z at late times, and, like SN 1988Z, it is a luminous X-ray source (both supernovae had an X-ray luminosity L_ X > 10^41 erg/s). The Halpha emission profile of SN 2008iy shows a narrow P Cygni absorption component, implying a pre-SN wind speed of ~100 km/s. We argue that the luminosity of SN 2008iy is powered via the interaction of the SN ejecta with a dense, clumpy circumstellar medium. The ~400 day rise time can be understood if the number density of clumps increases with distance over a radius ~1.7 x 10^16 cm from the progenitor. This scenario is possible if the progenitor experienced an episodic phase of enhanced mass-loss < 1 century prior to explosion or the progenitor wind speed increased during the decades before core collapse. We favour the former scenario, which is reminiscent of the eruptive mass-loss episodes observed for luminous blue variable (LBV) stars. The progenitor wind speed and increased mass-loss rates serve as further evidence that at least some, and perhaps all, Type IIn supernovae experience LBV-like eruptions shortly before core collapse. We also discuss the host galaxy of SN 2008iy, a subluminous dwarf galaxy, and offer a few reasons why the recent suggestion that unusual, luminous supernovae preferentially occur in dwarf galaxies may be the result of observational biases.