  We use the gauge unfixing (GU) formalism framework in a two dimensional
noncommutative chiral bosons (NCCB) model to disclose new hidden symmetries.
That amounts to converting a second-class system to a first-class one without
adding any extra degrees of freedom in phase space. The NCCB model has two
second-class constraints -- one of them turns out as a gauge symmetry generator
while the other one, considered as a gauge-fixing condition, is disregarded in
the converted gauge-invariant system. We show that it is possible to apply a
conversion technique based on the GU formalism direct to the second-class
variables present in the NCCB model, constructing deformed gauge-invariant GU
variables, a procedure which we name here as modified GU formalism. For the
canonical analysis in noncommutative phase space, we compute the deformed Dirac
brackets between all original phase space variables. We obtain two different
gauge invariant versions for the NCCB system and, in each case, a GU
Hamiltonian is derived satisfying a corresponding first-class algebra. Finally,
the phase space partition function is presented for each case allowing for a
consistent functional quantization for the obtained gauge-invariant NCCB.
