  We report initial results of the first flight of the Antarctic Impulsive
Transient Antenna (ANITA-1) 2006-2007 Long Duration Balloon flight, which
searched for evidence of a diffuse flux of cosmic neutrinos above energies of 3
EeV. ANITA-1 flew for 35 days looking for radio impulses due to the Askaryan
effect in neutrino-induced electromagnetic showers within the Antarctic ice
sheets. We report here on our initial analysis, which was performed as a blind
search of the data. No neutrino candidates are seen, with no detected physics
background. We set model-independent limits based on this result. Upper limits
derived from our analysis rule out the highest cosmogenic neutrino models. In a
background horizontal-polarization channel, we also detect six events
consistent with radio impulses from ultra-high energy extensive air showers.
