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The existence of methane in Titan's atmosphere (similar to 6% level at the surface) presents a unique enigma, as photochemical models predict that the current inventory will be entirely depleted by photochemistry in a timescale of similar to 20 Myr. In this paper, we examine the clues available from isotopic ratios (C-12/C-13 and D/H) in Titan's methane as to the past atmosphere history of this species. We first analyze recent infrared spectra of CH4 collected by the Cassini Composite Infrared Spectrometer, measuring simultaneously for the first time the abundances of all three detected minor isotopologues: (CH4)-C-13, (CH3D)-C-12, and (CH3D)-C-13. From these we compute estimates of C-12/C-13 = 86.5 +/- 8.2 and D/H = (1.59 +/- 0.33) x 10(-4), in agreement with recent results from the Huygens GCMS and Cassini INMS instruments. We also use the transition state theory to estimate the fractionation that occurs in carbon and hydrogen during a critical reaction that plays a key role in the chemical depletion of Titan's methane: CH4 + C2H -> CH3 + C2H2. Using these new measurements and predictions we proceed to model the time evolution of C-12/C-13 and D/H in Titan's methane under several prototypical replenishment scenarios. In our Model 1 (no resupply of CH4), we find that the present-day C-12/C-13 implies that the CH4 entered the atmosphere 60-1600 Myr ago if methane is depleted by chemistry and photolysis alone, but much more recently-most likely less than 10 Myr ago-if hydrodynamic escape is also occurring. On the other hand, if methane has been continuously supplied at the replenishment rate then the isotopic ratios provide no constraints, and likewise for the case where atmospheric methane is increasing. We conclude by discussing how these findings may be combined with other evidence to constrain the overall history of the atmospheric methane.