  We demonstrate that one-dimensional moir\'e patterns, analogous to those
found in twisted bilayer graphene, can arise in collapsed chiral carbon
nanotubes. Resorting to a combination of approaches, namely, molecular dynamics
to obtain the relaxed geometries and tight-binding calculations validated
against ab initio modeling, we find that magic angle physics occur in collapsed
carbon nanotubes. Velocity reduction, flat bands and localization in AA regions
with diminishing moir\'e angle are revealed, showing a magic angle close to
1$^{\rm o}$. From the spatial extension of the AA regions and the width of the
flat bands, we estimate that many-body interactions in these systems are
stronger than in twisted bilayer graphene. Chiral collapsed carbon nanotubes
stand out as promising candidates to explore many-body effects and
superconductivity in low dimensions, emerging as the one-dimensional analogues
of twisted bilayer graphene.
