In this work we describe the present status of an ongoing project to develop a Tandem-ElectroStatic-Quadrupole (TESQ) accelerator for Accelerator-Based (AB)-Boron Neutron Capture Therapy (BNCT) at the Atomic Energy Commission of Argentina in Buenos Aires. The project goal is a machine capable of delivering 30 mA of 2.4 MeV protons to be used in conjunction with a neutron production target based on the ⁷Li(p,n)⁷Be reaction slightly beyond its resonance at 2.25 MeV. These are the specifications needed to produce sufficiently intense and clean epithermal neutron beams, based on the ⁷Li(p,n)⁷Be reaction, to perform BNCT treatment for deep-seated tumors in less than an hour. An electrostatic machine is the technologically simplest and cheapest solution for optimized AB-BNCT. The machine being designed and constructed is a folded TESQ with a terminal at 1.2 MV. This machine is theoretically shown to be capable of transporting and accelerating a 30 mA proton beam to 2.4 MeV, using a 3D selfconsistent Poisson-Lorentz simulation code. The general geometric layout, its associated electrostatic fields, and the acceleration tube from ion source to neutron production target are calculated using a 3D finite element procedure. The design and construction of the ESQ modules is discussed and their electrostatic fields are investigated. Beam transport calculations through the accelerator are briefly mentioned. Likewise, work related to neutron production targets, strippers, beam shaping assembly and patient treatment room is briefly described.