  Based on CHANDRA observations of nearby starburst galaxies and RXTE/ASM, ASCA
and MIR-KVANT/TTM studies of high mass X-ray binary (HMXB) populations in the
Milky Way and Magellanic Clouds, we propose that the number and/or the
collective X-ray luminosity of HMXBs can be used to measure the star formation
rate (SFR) of a galaxy. We show that, within the accuracy of the presently
available data, a linear relation between HMXB number and the star formation
rate exists. The relation between SFR and collective luminosity of HMXBs is
non-linear in the low SFR regime, $L_X\propto \SFR^{\approx 1.7}$, and becomes
linear only for sufficiently high star formation rate, when the total number of
HMXB sources becomes sufficiently large. Such behaviour is caused by the fact,
that we measure collective luminosity of a population of the discrete sources.
Although more subtle SFR dependent effects are likely to exist, the data are
broadly consistent with the existence of a universal luminosity function of
HMXBs which can be roughly described as a power law with a differential slope
of $\sim 1.6$, a cutoff at $L_X \sim few \times 10^{40}$ erg/sec and a
normalisation proportional to the star formation rate.
  We apply our results to (spatially unresolved) starburst galaxies observed by
CHANDRA at redshifts up to $z\sim 1$ in the Hubble Deep Field North and show
that the calibration of the collective luminosity of HMXBs as a SFR indicator
based on the local sample agrees well with the SFR estimates obtained for these
distant galaxies with conventional methods.
