Star-forming compact dwarf galaxies (CDGs) resemble the expected pristine conditions of the first galaxies in the Universe and are the best systems to test models on primordial galaxy formation and evolution. Here, we report on one of such CDGs, Tololo 1214-277, which presents a broad, single peaked, highly symmetric Ly alpha emission line that had evaded theoretical interpretation so far. In this paper, we reproduce for the first time these line features with two different physically motivated kinematic models: an interstellar medium composed by outflowing clumps with random motions and an homogeneous gaseous sphere undergoing solid body rotation. The multiphase model requires a clump velocity dispersion of 54.3 +/- 0.6 km s(-1) with outflows of 54.3 +/- 5.1 km s(-1), while the bulk rotation velocity is constrained to be 348(-48)(+75) km s(-1). We argue that the results from the multiphase model provide a correct interpretation of the data. In that case, the clump velocity dispersion implies a dynamical mass of 2 x 10(9) M-circle dot, 10 times its baryonic mass. If future kinematic maps of Tololo 1214-277 confirm the velocities suggested by the multiphase model, it would provide additional support to expect such kinematic state in primordial galaxies, opening the opportunity to use the models and methods presented in this paper to constrain the physics of star formation and feedback in the early generation of Ly alpha - emitting galaxies.