  Weyl fermions are a new ingredient for correlated states of electronic
matter. A key difficulty has been that real materials also contain non-Weyl
quasiparticles, and disentangling the experimental signatures has proven
challenging. We use magnetic fields up to 95 tesla to drive the Weyl semimetal
TaAs far into its quantum limit (QL), where only the purely chiral 0th Landau
levels (LLs) of the Weyl fermions are occupied. We find the electrical
resistivity to be nearly independent of magnetic field up to 50 tesla: unusual
for conventional metals but consistent with the chiral anomaly for Weyl
fermions. Above 50 tesla we observe a two-order-of-magnitude increase in
resistivity, indicating that a gap opens in the chiral LLs. Above 80 tesla we
observe strong ultrasonic attenuation below 2 kelvin, suggesting a
mesoscopically-textured state of matter. These results point the way to
inducing new correlated states of matter in the QL of Weyl semimetals.
