The existence of methane in Titan's atmosphere (∼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 ∼20Myr. In this paper, we examine the clues available from isotopic ratios (12C/13C 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: 13CH4, 12CH3D, and 13CH3D. From these we compute estimates of 12C/13C= 86.5 ± 8.2 and D/H= (1.59 ± 0.33) × 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 12C/13C and D/H in Titan's methane under several prototypical replenishment scenarios. In our Model1 (no resupply of CH4), we find that the present-day 12C/13C implies that the CH4 entered the atmosphere 60-1600Myr ago if methane is depleted by chemistry and photolysis alone, but much more recently - most likely less than 10Myr 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. © 2012 The American Astronomical Society. All rights reserved.