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A new design for the anode of a time projection chamber, consisting of a charge-detecting "tile", is investigated for use in the proposed tonne-scale nEXO experiment to search for neutrinoless double-beta decay.  Modular by design, an array of tiles can cover a sizable area. The width of each strip is small compared to the size of the tile, so a Frisch grid is not required. A grid-less, tiled anode design is beneficial for an experiment such as nEXO, where a wire tensioning support structure and Frisch grid might contribute radioactive backgrounds and would have to be designed to accommodate cycling to cryogenic temperatures.   A prototype tile was tested in a cell containing liquid xenon. Very good agreement is achieved between the measured ionization spectrum of a 207Bi source and simulations giving an energy resolution comparable to the best intrinsic ionization-only resolution necessary to achieve the expected energy resolution σ/Qββ of 1 %.