It is assumed that the radioactive decay of 44Ti powers the infrared, optical and ultraviolet emission of supernova remnants after the complete decay of 56Co and 57Co (the isotopes that dominated the energy balance during the first three to four years after the explosion) until the beginning of active interaction of the ejecta with the surrounding matter. Simulations show that the initial mass of 44Ti synthesized in core-collapse supernovae is (0.02-2.5) × 10-4 solar masses (). Hard X-rays and γ-rays from the decay of this 44Ti have been unambiguously observed from Cassiopeia A only, leading to the suggestion that values of the initial mass of 44Ti near the upper bound of the predictions occur only in exceptional cases. For the remnant of supernova 1987A, an upper limit to the initial mass of 44Ti of <10-3 has been obtained from direct X-ray observations, and an estimate of (1-2) × 10-4 has been made from infrared light curves and ultraviolet spectra by complex and model-dependent computations. Here we report observations of hard X-rays from the remnant of supernova 1987A in the narrow band containing two direct-escape lines of 44Ti at 67.9 and 78.4 keV. The measured line fluxes imply that this decay provided sufficient energy to power the remnant at late times. We estimate that the initial mass of 44Ti was (3.1 +/- 0.8) × 10-4, which is near the upper bound of theoretical predictions.