In the Milky Way, most globular clusters are highly conspicuous objects that were found centuries ago. However, a few dozen of them are faint, sparsely populated systems that were identified largely during the second half of the past century. One of the faintest is ESO 37-1 (E 3) and as such it remains poorly studied, with no spectroscopic observations published so far although it was discovered in 1976. We investigate the globular cluster E3 in an attempt to better constrain its fundamental parameters. Spectroscopy of stars in the field of E3 is shown here for the first time. Deep, precise VI CCD photometry of E3 down to V~26mag is presented and analysed. Low-resolution, medium signal-to-noise ratio spectra of nine candidate members are studied to derive radial velocity and metallicity. Proper motions from the UCAC4 catalogue are used to explore the kinematics of the bright members of E3. Isochrone fitting indicates that E3 is probably very old, with an age of about 13Gyr; its distance from the Sun is nearly 10kpc. It is also somewhat metal rich with [Fe/H]=-0.7. Regarding its kinematics, our tentative estimate for the proper motions is ({mu}_{alpha}*cos{delta}, {mu}_{delta}_=(-7.0+/-0.8, 3.5+/-0.3)mas/yr (or a tangential velocity of 382+/-79km/s) and for the radial velocity 45+/-5km/s in the solar rest frame. E3 is one of the most intriguing globular clusters in the Galaxy. Having an old age and being metal rich is clearly a peculiar combination, only seen in a handful of objects like the far more conspicuous NGC 104 (47 Tucanae). In addition, its low luminosity and sparse population make it a unique template for the study of the final evolutionary phases in the life of a star cluster. Unfortunately, E3 is among the most elusive and challenging known globular clusters because field contamination severely hampers spectroscopic studies.