The mass and chemical composition of a star are the primary determinants of its basic physical properties-radius, temperature and luminosity-and how those properties evolve with time. Accordingly, two stars born at the same time, from the same natal material and with the same mass, are 'identical twins,' and as such might be expected to possess identical physical attributes. We have discovered in the Orion nebula a pair of stellar twins in a newborn binary star system. Each star in the binary has a mass of 0.41 +/- 0.01 solar masses, identical to within 2 per cent. Here we report that these twin stars have surface temperatures differing by approximately 300 K ( approximately 10 per cent) and luminosities differing by approximately 50 per cent, both at high confidence level. Preliminary results indicate that the stars' radii also differ, by 5-10 per cent. These surprising dissimilarities suggest that one of the twins may have been delayed by several hundred thousand years in its formation relative to its sibling. Such a delay could only have been detected in a very young, definitively equal-mass binary system. Our findings reveal cosmic limits on the age synchronization of young binary stars, often used as tests for the age calibrations of star-formation models.