  The supernova (SN) delay-time distribution (DTD) - the SN rate versus time
that would follow a brief burst of star formation - can shed light on SN
progenitors, and on chemical enrichment timescales. Previous attempts to
recover the DTD have used comparisons of mean SN rates vs. redshift to cosmic
star-formation history (SFH), or comparison of SN rates among galaxies of
different mean ages. We present an approach to recover the SN DTD that avoids
such averaging. We compare the SFHs of individual galaxies to the numbers of
SNe discovered in each galaxy (generally zero, sometimes one or a few SNe). We
apply the method to a subsample of 3505 galaxies, hosting 82 SNe Ia and 119
core-collapse SNe (CC SNe), from the Lick Observatory SN Search (LOSS), with
SFHs reconstructed from SDSS spectra. We find a >2sigma SN Ia DTD signal in our
shortest-delay, "prompt", bin at <420 Myr. Despite a systematic error, due to
the limited aperture of the SDSS spectroscopic fibres, which causes some of the
prompt signal to leak to the later DTD bins, the data require prompt SNe Ia at
the >99% confidence. We further find, at 4sigma, SNe Ia that are "delayed" by >
2.4 Gyr. Thus, the data support the existence of both prompt and delayed SNe
Ia. The time integral over the CC SN DTD is 0.010+/-0.002 SNe per Msun, as
expected if all stars of mass >8 Msun lead to visible SN explosions. This
argues against a minimum mass for CC SNe of >10 Msun, and against a significant
fraction of massive stars that collapse without exploding. For SNe Ia, the
time-integrated DTD is 0.0023+/-0.0006 SNe per Msun formed, most of them with
delays < 2.4 Gyr. We show, using simulations, that application of the method to
the full existing LOSS sample, but with complete and unbiased SFH estimates for
the survey galaxies, could provide a detailed measurement of the SN Ia DTD.
