  Massive galaxy clusters at intermediate redshift can magnify the flux of
distant background sources by several magnitudes and we exploit this effect to
search for lensed distant supernovae that may otherwise be too faint to be
detected. A supernova search was conducted at near infrared wavelengths using
the ISAAC instrument at the VLT. The galaxy clusters Abell 1689, Abell 1835 and
AC114 were observed at multiple epochs of 2 hours of exposure time, separated
by a month. Image-subtraction techniques were used to search for transient
objects with light curve properties consistent with supernovae, both in our new
and archival ISAAC/VLT data. The limiting magnitude of the individual epochs
was estimated by adding artificial stars to the subtracted images. Most of the
epochs reach 90% detection efficiency at SZ(J) ~= 23.8-24.0 mag (Vega). Two
transient objects, both in archival images of Abell 1689 and AC114, were
detected. The transient in AC114 coincides - within the position uncertainty -
with an X-ray source and is likely to be a variable AGN at the cluster
redshift. The transient in Abell 1689 was found at SZ=23.24 mag, ~0.5 arcsec
away from a galaxy with photometric redshift z=0.6 +/-0.15. The light curves
and the colors of the transient are consistent with a reddened Type IIP
supernova at redshift z=0.59 +/- 0.05. The lensing model of Abell 1689 predicts
~1.4 mag of magnification at the position of the transient, making it the most
magnified supernova ever found and only the second supernova found behind a
galaxy cluster. Our pilot survey has demonstrated the feasibility to find
distant gravitationally magnified supernovae behind massive galaxy clusters.
One likely supernova was found behind Abell 1689, in accordance with the
expectations for this survey, as shown in an accompanying analysis paper.
