Since its start of data taking, the LHC has provided an impressive wealth of information on the quark and gluon structure of the proton. Indeed, modern global analyses of parton distribution functions (PDFs) include a wide range of LHC measurements of processes such as the production of jets, electroweak gauge bosons, and top quark pairs. In this work, we assess the ultimate constraining power of LHC data on the PDFs that can be expected from the complete dataset, in particular after the High-Luminosity (HL) phase, starting in around 2025. The huge statistics of the HL-LHC, delivering L=3ab-1 to ATLAS and CMS and L=0.3ab-1 to LHCb, will lead to an extension of the kinematic coverage of PDF-sensitive measurements as well as to an improvement in their statistical and systematic uncertainties. Here we generate HL-LHC pseudo-data for different projections of the experimental uncertainties, and then quantify the resulting constraints on the PDF4LHC15 set by means of the Hessian profiling method. We find that HL-LHC measurements can reduce PDF uncertainties by up to a factor of 2 to 4 in comparison to state-of-the-art fits, leading to few-percent uncertainties for important observables such as the Higgs boson transverse momentum distribution via gluon-fusion. Our results illustrate the significant improvement in the precision of PDF fits achievable from hadron collider data alone, and motivate the continuation of the ongoing successful program of PDF-sensitive measurements by the LHC collaborations.