  Topological semimetals in chiral crystals, which possess both structural
handedness and band crossings (or nodes) with topological chiral charge,
exhibit many exotic physical properties. Here we demonstrate that the
structural and electronic chirality of these systems can endow them with
another fascinating phenomenon -- the intrinsic nonlinear planar Hall effect
(INPHE), which is prominent around the nodes and reverses sign upon chirality
reversal in opposite enantiomers. Taking chiral tellurium as an example, we
reveal an intrinsic orbital mechanism, which manifests diverging orbital
magnetic moments with hedgehog-like textures around nodes and, therefore,
generates a dominant contribution to the INPHE that is proportional to the
topological charge. Furthermore, we show that multifold fermions in topological
chiral semimetals with B20 structures (e.g., CoSi and PtAl) induce a giant
INPHE conductivity reaching the order of $1\sim 10\;
\mathrm{A}\cdot\mathrm{V}^{-2}\cdot\mathrm{T}^{-1}$, which is detectable in
experiments. Our study not only relates nonlinear transport to band topology
and enantiomer recognition but also offers a new way to explore the exotic
physical properties associated with unconventional chiral fermions.
