We present the first study of the phase diagram of a thick film of superfluid 3He confined within a nanofabricated slab geometry. This cryogenic microfluidic chamber provides a well-defined environment for the superfluid, in which both the regular geometry and surface roughness may be fully characterised. The chamber is designed with a slab thickness d=0.6 μm and 3 mm thick walls to allow pressure tuning of the effective confinement between 0 and 5.5 bar. Over this range the zero temperature superfluid coherence length, ξ 0, decreases by approximately a factor of two from 77 to 40 nm. Samples have so far been cooled to 350 μK. We use nuclear magnetic resonance (NMR) to 'finger-print' the superfluid order parameter, with the static field applied perpendicular to the slab. To enable us to resolve high quality NMR signals from the tiny amount of superfluid 3He in the slab, we have developed a spectrometer using a two stage SQUID amplifier with unprecedented sensitivity. Simple NMR zeugmatography allows the slab signal to be unambiguously distinguished from that of a small bulk liquid region near the fill line. The measured slab transition temperature, T c slab, shows a suppression proportional to ξ 0 2, as expected theoretically, but the absolute suppression is less than expected. Below T c slab, an A-like phase is stable over a significant temperature range. A transition temperature, T AX, is measured on warming from a so far unidentified phase, occurring at lower temperatures, into the A-phase. At the pressures investigated (3 to 5.5 bar) the transition appears to occur at an approximately fixed value of the effective confinement d/ξ(T AX ). In this geometry we predict that the A-phase will be stable to T=0 at zero pressure. © 2009 Springer Science+Business Media, LLC.