  Spiral galaxies have distinct internal structures including a stellar bulge,
disk and spiral arms. It is unknown when in cosmic history these structures
formed. We analyze observations of BRI 1335-0417, an intensely star-forming
galaxy in the distant Universe, at redshift 4.41. The [C II] gas kinematics
show a steep velocity rise near the galaxy center and have a two-armed spiral
morphology that extends from about 2 to 5 kiloparsecs in radius. We interpret
these features as due to a central compact structure, such as a bulge, a
rotating gas disk and either spiral arms or tidal tails. These features had
been formed within 1.4 billion years after the Big Bang, long before the peak
of cosmic star formation.
