  We present the orbital solution for the donor star of the candidate
transitional millisecond pulsar 3FGL J1544.6-1125, currently observed as an
accreting low-mass X-ray binary. The orbital period is $0.2415361(36)$ days,
entirely consistent with the spectral classification of the donor star as a mid
to late K dwarf. The semi-amplitude of the radial velocity curve is
exceptionally low at $K_2=39.3\pm1.5$ km s$^{-1}$, implying a remarkably
face-on inclination in the range 5--8$^{\circ}$, depending on the neutron star
and donor masses. After determining the veiling of the secondary, we derive a
distance to the binary of $3.8\pm0.7$ kpc, yielding a 0.3--10 keV X-ray
luminosity of $6.1\pm1.9\times10^{33}\,{\rm erg\,s^{-1}}$, similar to confirmed
transitional millisecond pulsars. As face-on binaries rarely occur by chance,
we discuss the possibility that Fermi-selected samples of transitional
milli-second pulsars in the sub-luminous disk state are affected by beaming. By
phasing emission line strength on the spectroscopic ephemeris, we find coherent
variations, and argue that these variations are most consistent with emission
from an asymmetric shock originating near the inner disk.
