  We present the results from an ESO/VLT campaign aimed at studying the
afterglow properties of the short/hard gamma ray burst GRB 070707. Observations
were carried out at ten different epochs from ~0.5 to ~80 days after the event.
The optical flux decayed steeply with a power-law decay index greater than 3,
later levelling off at R~27.3 mag; this is likely the emission level of the
host galaxy, the faintest yet detected for a short GRB. Spectroscopic
observations did not reveal any line features/edges that could unambiguously
pinpoint the GRB redshift, but set a limit z < 3.6. In the range of allowed
redshifts, the host has a low luminosity, comparable to that of long-duration
GRBs. The existence of such faint host galaxies suggests caution when
associating short GRBs with bright, offset galaxies, where the true host might
just be too dim for detection. The steepness of the decay of the optical
afterglow of GRB 070707 challenges external shock models for the optical
afterglow of short/hard GRBs. We argue that this behaviour might results from
prolonged activity of the central engine or require alternative scenarios.
