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We develop an asymptotic theory for the front speed in a cellular flow in the limit of small molecular diffusivity and fast reaction, i.e., large P\\'eclet ($Pe$) and Damk\\\"ohler ($Da$) numbers. The front speed is expressed in terms of a periodic path -- an instanton -- that minimizes a certain functional. This leads to an efficient procedure to calculate the front speed, and to closed-form expressions for $(\\log Pe)^{-1}\\ll Da\\ll Pe$ and for $Da\\gg Pe$. 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