High-resolution angle-resolved photoemission data from the insulating phase of the charge-density-wave (CDW) material 1T-TaS2 reveal the backfolding of the electronic bands associated with the CDW superlattice, but also an additional, unexpected periodicity. This periodicity is consistent with the dispersion predicted at zero temperature if three-sublattice magnetic order is present, suggesting that it is the signature of fluctuations associated with magnetic ordering of a Mott insulator on a triangular lattice.