We present precision neutron scattering measurements of the Bose-Einstein condensate fraction, n0(T), and the atomic momentum distribution, nstar(k), of liquid 4He at pressure p =24 bar. Both the temperature dependence of n0(T) and of the width of nstar(k) are determined. The n0(T) can be represented by n0(T) = n0(0)[1-(T/T{lambda}){gamma}] with a small n0(0) = 2.80pm0.20% and large {gamma} = 13pm2 for T < T{lambda} indicating strong interaction. The onset of BEC is accompanied by a significant narrowing of the nstar(k). The narrowing accounts for 65% of the drop in kinetic energy below T{lambda} and reveals an important coupling between BEC and k > 0 states. The experimental results are well reproduced by Path Integral Monte Carlo calculations.
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