  We investigate the effect of the electric-charge neutrality in
  $\beta$ equilibrium on the chiral phase transition by solving the chiral and
diquark condensates in the two-flavor Nambu--Jona-Lasinio model. We demonstrate
that the electric-charge neutrality plays a similar role as the repulsive
vector interaction; they both weaken the first-order chiral phase transition in
the high-density and low-temperature region. The first-order chiral phase
transition is not affected, however, at finite temperatures where the diquark
condensate melts. In this way the chiral phase transition could be second-order
at intermediate temperatures if the diquark effects overwhelm the chiral
dynamics, while the first-order transition may survive at lower and higher
temperatures. The number of the critical points appearing on the phase diagram
can vary from zero to three, which depends on the relative strength of the
chiral and diquark couplings. We systematically study the possibility of the
phase structure with multiple QCD critical points and evaluate the Meissner
screening mass to confirm that our conclusion is not overturned by
chromomagnetic instability.
