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We show how it is possible to make a self-reproducing cell in an artificial chemistry by surrounding a replicating molecule with a semi-permeable membrane. The molecule can carry an arbitrary amount of information, encoded in a material form as a sequence of bases, as in DNA. The cells produce enzymes through a decoding of their base sequence, and these enzymes trigger reactions essential to the cell's survival. Earlier work in a similar artificial chemistry showed that replicators free in solution could obtain no survival advantage from producing enzymes; here we show that when surrounded by a membrane the replicators can obtain an advantage. We show that the cells reliably reproduce over many generations under environmental pressure for resources. By creating cells in a material-based artificial chemistry we hope that the system might have the potential for open-ended, creative evolution.