Schizophrenia, a psychiatric disorder, is a condition of core cognitive defects partly due to reductions in gamma oscillations. Gamma oscillations (20-80Hz) are neural correlates of certain cognitive effects. They are created by the Pyramidal Interneuron Network Gamma containing inhibitory, excitatory and chandelier cells. Post-mortem schizophrenic brains have shown a reduction in synaptic connectivity of inhibitory and excitatory cells, and an increase in chandelier connectivity. We hypothesize that an increase in chandelier cell connectivity can compensate for the reduction in other synapses. Using the integrate-and-fire equations, we derive a firing rate model and later extend to a spiking model to test this hypothesis. We find that within a certain range of reversal potential and strength, chandelier cells have the ability to compensate for the reduction of both inhibition and excitation; and return the system to firing gamma oscillations.