High spin states in 135Ce were studied following the 124Sn(16O, 5n)135Ce reaction with an array of 8 Compton suppressed clover detectors and a multiplicity filter consisting of 14 NaI(T1) detectors. The decay scheme of 135Ce shows a pair of ΔI = 1 bands which have nearly degenerate energies. The levels in two bands cross each other near the band head spin and again close to the highest spin. Both these bands have similar intensity and moment of inertia. Inter-band transitions have been observed in both directions. Both the bands have also similar B(M1)/B(E2) ratios with increasing rotational frequency. Lifetimes of levels up to a spin of 41/2 have been measured to obtain inband B(M1), B(E2) values and the ratios of the infra band and inter band B(M1) values. It has been concluded from the present observations that these bands may form a `Chiral doublet' in 135Ce.
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