We use a sample of 97 galaxies selected from the ALFALFA 21cm survey to make an accurate measurement of the baryonic Tully-Fisher relation (BTFR). These galaxies are specifically selected to be heavily gas-dominated (Mgas/M* >~ 2.7) and to be oriented edge-on. The former property ensures that the error on the galactic baryonic mass is small, despite the large systematic uncertainty involved in galactic stellar mass estimates. The latter property means that rotational velocities can be derived directly from the width of the 21cm emission line, without any need for inclination corrections. We measure a slope for the linewidth-based BTFR of alpha = 3.75 +- 0.11, a value that is somewhat steeper than (but in broad agreement with) previous literature results. The relation is remarkably tight, with almost all galaxies being located within a perpendicular distance of +- 0.1 dex from the best fit line. The low observational error budget for our sample enables us to establish that, despite its tightness, the measured linewidth-based BTFR has some small (i.e., non-zero) intrinsic scatter. We furthermore find a systematic difference in the BTFR of galaxies with double-horned 21cm line profiles and those with peaked profiles. When we restrict our sample of galaxies to objects in the former category, we measure a slightly steeper slope of alpha = 4.13 +- 0.15. Overall, the high-accuracy measurement of the BTFR presented in this article is intended as a reliable observational benchmark against which to test theoretical expectations. Here we consider a representative set of semi-analytic models and hydrodynamic simulations in the LCDM context, as well as MOND. In the near future, interferometric follow-up observations of several sample members will enable us to further refine the BTFR measurement, and make sharper comparisons with theoretical models.
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