Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high-temperature superconductivity. By contrast, the parent phase of an iron-based high-temperature superconductor is never a correlated insulator. However, this distinction may be deceptive because Fe has five actived d orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund's metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations, producing orbitally selective strong correlations. The spectral weights Z(m) of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle Z(m) appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that Z(xy) < Z(xz) << Z(yz), consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based high-temperature superconductivity in FeSe.