The Critical Heat Flux (CHF) of water with dispersed alumina nanoparticles was measured for the geometry and flow conditions relevant to the In-Vessel Retention (IVR) situation which can occur during core melting sequences in certain advanced Light Water Reactors (LWRs). CHF measurements were conducted in a flow boiling loop featuring a test section designed to be thermal-hydraulically similar to the vessel/insulation gap in the Westinghouse AP1000 plant. The effects of orientation angle, pressure, mass flux, fluid type, boiling time, surface material, and surface state were investigated. Results for water-based nanofluids with alumina nanoparticles (0.001% by volume) on stainless steel surface indicate an average 70% CHF enhancement with a range of 17% to 108% depending on the specific flow conditions expected for IVR. Experiments also indicate that only about thirty minutes of boiling time (which drives nanoparticle deposition) are needed to obtain substantial CHF enhancement with nanofluids.