The Dirac equation can be derived from the transformation properties of spin-1/2 systems under pure boosts. This derivation is presented Ryder's Quantum Field Theory. However, the derivation of a similar equation for spin-1 systems is not given. Following the same steps as in Ryder for the Dirac equation I have tried to work out the derivation of the equation that relates the two different parts of a two-component spin-1 system in chiral representation. I have also derived Maxwell’s equations from it. I am not sure whether the derivation is right, as it is not available in any of my references. I would appreciate any comments or any discussion about it: http://www.geocities.com/alschairn/diracmaxwell/diracmaxwell.htm It is a bit long, but most of the steps are very easy to follow.