We have discovered a 300 kpc-wide giant Lyman-alpha (Ly alpha) nebula centered on the massive galaxy group RO-1001 at z=2.91 in the Cosmic Evolution Survey field. Keck Cosmic Web Imager observations reveal three cold gas filaments converging into the center of the potential well of its similar to 4x10(13)M(circle dot) dark matter halo, hosting 1200 M-circle dot yr(-1) of star formation as probed by Atacama Large Millimeter Array and NOrthern Extended Millimeter Array observations. The nebula morphological and kinematics properties and the prevalence of blueshifted components in the Ly alpha spectra are consistent with a scenario of gas accretion. The upper limits on active galactic nuclei activity and overall energetics favor gravity as the primary Ly alpha powering source and infall as the main source of gas flows to the system. Although interpretational difficulties remain, with outflows and likely also photoionization with ensuing recombination still playing a role, this finding provides arguably an ideal environment to quantitatively test models of cold gas accretion and galaxy feeding inside an actively star-forming massive halo at high redshift.