A new design for the anode of a time projection chamber, consisting of a charge-detecting tile, is investigated for use in large scale liquid xenon detectors. The tile is produced by depositing 60 orthogonal metal charge-collecting strips, 3~mm wide, on a 10~si{cm} $times$ 10~si{cm} fused-silica wafer. These charge tiles may be employed by large detectors, such as 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. The segmented anode also reduces some degeneracies in signal reconstruction that arise in large-area crossed-wire time projection chambers. A prototype tile was tested in a cell containing liquid xenon. Very good agreement is achieved between the measured ionization spectrum of a $^{207}$Bi source and simulations that include the microphysics of recombination in xenon and a detailed modeling of the electrostatic field of the detector. An energy resolution $sigma/E$=5.5% is observed at 570~si{keV}, comparable to the best intrinsic ionization-only resolution reported in literature for liquid xenon at 936~V/si{cm}.
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