The growth of supermassive black holes appears to be driven by galaxy mergers, violent merger-free processes and/or 'secular' processes. In order to quantify the effects of secular evolution on black hole growth, we study a sample of active galactic nuclei (AGN) in galaxies with a calm formation history free of significant mergers, a population that heretofore has been difficult to locate. Here we present an initial sample of 13 AGN in massive (M* ≳ 1010M⊙) bulgeless galaxies - which lack the classical bulges believed inevitably to result from mergers - selected from the Sloan Digital Sky Survey using visual classifications from Galaxy Zoo. Parametric morphological fitting confirms that the host galaxies lack classical bulges; any contributions from pseudo-bulges are very small (typically <5 per cent). We compute black hole masses for the two broad-line objects in the sample (4.2 × 106 and 1.2 × 107M⊙) and place lower limits on black hole masses for the remaining sample (typically MBH ≳ 106M⊙), showing that significant black hole growth must be possible in the absence of mergers or violent disc instabilities. The black holemasses are systematically higher than expected from established bulge-black hole relations. However, if the mean Eddington ratio of the systems with measured black hole masses (L/LEdd̃0.065) is typical, 10 of 13 sources are consistent with the correlation between black hole mass and total stellar mass. That pure disc galaxies and their central black holes may be consistent with a relation derived from elliptical and bulge-dominated galaxies with very different formation histories implies the details of stellar galaxy evolution and dynamics may not be fundamental to the co-evolution of galaxies and black holes.