We present a long (~76 ks) Chandra observation of IRAS 09104+4109, a hyper-luminous galaxy, optically classified as a Type 2 AGN hosted in a cD galaxy in a cluster at z=0.442. We also report on the results obtained by fitting its broad-band spectral energy distribution. The Compton-thick nature of this source (which has been often referred to as an archetype of Compton-thick Type 2 quasars) was formerly claimed on the basis of its marginal detection in the PDS instrument onboard BeppoSAX, being then disputed using XMM-Newton data. Both Chandra analysis and optical/mid-IR spectral fitting are consistent with the presence of heavy (~1-5 10^{23} cm^{-2}) but not extreme (Compton-thick) obscuration. However, using the mid-IR and the [OIII] emission as proxies of the nuclear hard X-ray luminosity suggests the presence of heavier obscuration. The 54-month Swift BAT map shows excess hard X-ray emission likely related to a nearby (z=0.009) Type 2 AGN, close enough to IRAS 09104+4109 to significantly enhance and contaminate its emission in the early BeppoSAX PDS data.