A monolithic pixel sensor with high spatial granularity (35 × 40 μm2) is presented, aiming at thermal neutron detection and imaging. The device is made using the CMOS SOIPIX technology, with Deep Reactive-Ion Etching post-processing on the backside to obtain high aspect-ratio cavities that will be filled with neutron converters. This is the first monolithic 3D sensor ever reported. Owing to the microstructured backside, a neutron detection efficiency up to 30% can be achieved with a10B converter, as estimated by the Geant4 simulations. Each pixel includes circuitry that allows a large dynamic range and energy discrimination and charge-sharing information between neighboring pixels, with a power dissipation of 10 µW per pixel at 1.8 V power supply. The initial results from the experimental characterization of a first test-chip prototype (array of 25 × 25 pixels) in the laboratory are also reported, dealing with functional tests using alpha particles with energy compatible with the reaction products of neutrons with the converter materials, which validate the device design.