  We introduce a particle-hole-symmetric metallic state of bosons in a magnetic
field at odd-integer filling. This state hosts composite fermions whose energy
dispersion features a quadratic band touching and corresponding $2\pi$ Berry
flux protected by particle-hole and discrete rotation symmetries. We also
construct an alternative particle-hole symmetric state---distinct in the
presence of inversion symmetry---without Berry flux. As in the Dirac composite
Fermi liquid introduced by Son, breaking particle-hole symmetry recovers the
familiar Chern-Simons theory. We discuss realizations of this phase both in 2D
and on bosonic topological insulator surfaces, as well as signatures in
experiments and simulations.
