  The ALMA interferometer, with its unprecedented combination of
high-sensitivity and high-angular resolution, allows for (sub-)mm wavelength
mapping of protostellar systems at Solar System scales. Astrochemistry has
benefited from imaging interstellar complex organic molecules in these jet-disk
systems. Here we report the first detection of methanol (CH3OH) and methyl
formate (HCOOCH3) emission towards the triple protostellar system VLA1623-2417
A1+A2+B, obtained in the context of the ALMA Large Program FAUST. Compact
methanol emission is detected in lines from Eu = 45 K up to 61 K and 537 K
towards components A1 and B, respectively. LVG analysis of the CH3OH lines
towards VLA1623-2417 B indicates a size of 0.11-0.34 arcsec (14-45 au), a
column density N(CH3OH) = 10^16-10^17 cm-2, kinetic temperature > 170 K, and
volume density > 10^8 cm-3. An LTE approach is used for VLA1623-2417 A1, given
the limited Eu range, and yields Trot < 135 K. The methanol emission around
both VLA1623-2417 A1 and B shows velocity gradients along the main axis of each
disk. Although the axial geometry of the two disks is similar, the observed
velocity gradients are reversed. The CH3OH spectra from B shows two broad (4-5
km s-1) peaks, which are red- and blue-shifted by about 6-7 km s-1 from the
systemic velocity. Assuming a chemically enriched ring within the accretion
disk, close to the centrifugal barrier, its radius is calculated to be 33 au.
The methanol spectra towards A1 are somewhat narrower (about 4 km s-1),
implying a radius of 12-24 au.
