A search for a massive WPRIME gauge boson is performed with the ATLAS detector at the LHC in P P collisions at a centre-of-mass energy of sqrt(s) = 8 TeV, corresponding to 20.3 fb-1 of integrated luminosity. This analysis is done in the WPRIME --> TOP BOTTOM --> QUARK QUARK BOTTOM BOTTOM mode for WPRIME masses above 1.5 TeV, where the WPRIME decay products are highly boosted. Novel jet substructure techniques are used to identify jets from high-momentum top quarks to ensure high sensitivity, independent of WPRIME mass, up to 3 TeV; b-tagging is also used to identify jets originating from b-quarks. The data are consistent with Standard Model background-only expectations, and upper limits at 95% confidence level are set on the WPRIME --> TOP BOTTOM cross section times branching ratio ranging from 0.16 pb to 0.33 pb for left-handed WPRIME bosons, and ranging from 0.10 pb to 0.21 pb for WPRIME bosons with purely right-handed couplings. Upper limits at 95% confidence level are set on the WPRIME-boson coupling to TOP BOTTOM as a function of the WPRIME mass using an effective field theory approach, which is independent of details of particular models predicting a WPRIME boson.