  Observations of the cosmic microwave background indicate that baryons account
for 5% of the Universe's total energy content. In the local Universe, the
census of all observed baryons falls short of this estimate by a factor of two.
Cosmological simulations indicate that the missing baryons might not have
condensed into virialized haloes, but reside throughout the filaments of the
cosmic web (where matter density is larger than average) as a low-density
plasma at temperatures of $10^5-10^7$ kelvin, known as the warm-hot
intergalactic medium. There have been previous claims of the detection of warm
baryons along the line of sight to distant blazars and of hot gas between
interacting clusters. These observations were, however, unable to trace the
large-scale filamentary structure, or to estimate the total amount of warm
baryons in a representative volume of the Universe. Here we report X-ray
observations of filamentary structures of gas at $10^7$ kelvin associated with
the galaxy cluster Abell 2744. Previous observations of this cluster were
unable to resolve and remove coincidental X-ray point sources. After
subtracting these, we reveal hot gas structures that are coherent over scales
of 8 mergaparsecs. The filaments coincide with over-densities of galaxies and
dark matter, with 5-10% of their mass in baryonic gas. This gas has been heated
up by the cluster's gravitational pull and is now feeding its core. Our
findings strengthen evidence for a picture of the Universe in which a large
fraction of the missing baryons reside in the filaments of the cosmic web.
