We derive age constraints for 1639 red giants in the APOKASC sample for which seismic parameters from Kepler, as well as effective temperatures, metallicities and [α/Fe] values from APOGEE DR12 (Apache Point Observatory Galactic Evolution Experiment Data Release 12) are available. We investigate the relation between age and chemical abundances for these stars, using a simple and robust approach to obtain ages. We first derive stellar masses using standard seismic scaling relations, then determine the maximum possible age for each star as function of its mass and metallicity, independently of its evolutionary stage. While the overall trend between maximum age and chemical abundances is a declining fraction of young stars with increasing [α/Fe], at least 14 out of 241 stars with [α/Fe] >0.13 are younger than 6 Gyr. Five stars with [α/Fe] ≥0.2 have ages below 4 Gyr. We examine the effect of modifications in the standard seismic scaling relations, as well as the effect of very low helium fractions, but these changes are not enough to make these stars as old as usually expected for α-rich stars (i.e. ages greater than 8-9 Gyr). Such unusual α-rich young stars have also been detected by other surveys, but defy simple explanations in a galaxy evolution context.