We present the results of a 47-ks Chandra-ACIS observation of the old open cluster M67. We detected 25 proper-motion cluster members (including ten new sources) and 12 sources (all new) that we suspect to be members from their locations close to the main sequence (1 < B-V < 1.7). Of the detected members, 23 are binaries. Among the new sources that are members and probable members are four spectroscopic binaries with P_orb < 12 d, two contact binaries and two periodic photometric variables with P_ph < 8.4 d. Their X-rays are likely the result of coronal activity enhanced by tidally locked rapid rotation. The X-rays of the new source S997, a blue straggler in a wide eccentric orbit, are puzzling. Spectral fits show that the X-rays of the brightest sources S1063 (a binary with a sub-subgiant), S1082 (a triple blue straggler with a close binary) and S1040 (a circular binary of a giant and a cool white dwarf), are consistent with coronal emission. We detected a new bright source that must have brightened at least about ten times since the time of the ROSAT observations. It is not clear whether its faint blue optical counterpart belongs to M67. We discuss the possibility that this source is a low-mass X-ray binary in quiescence, which would be the first of its kind in an open cluster. In addition to cluster members, we detected about 100 background sources, many of which we identify with faint objects in the ESO Imaging Survey.