Persistent gravitational waves from rapidly rotating neutron stars, such as those found in some young supernova remnants, may fall in the sensitivity band of the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO). Searches for these signals are computationally challenging, as the frequency and frequency derivative are unknown and evolve rapidly due to the youth of the source. A hidden Markov model (HMM), combined with a maximum-likelihood matched filter, tracks rapid frequency evolution semi-coherently in a computationally efficient manner. We present the results of an HMM search targeting 12 young supernova remnants in data from Advanced LIGOs second observing run. Six targets produce candidates that are above the search threshold and survive pre-defined data quality vetoes. However, follow-up analyses of these candidates show that they are all consistent with instrumental noise artefacts.