After Einstein's experiments of the 20th century we now know this to be not strictly true, as any energy change must also engender a change in mass. However, the mass change in chemical reactions is so tiny as to be effectively zero.
Einstein related the energy change to the mass multiplied by the speed of light (3 x 108 ms-1) squared:
E = mc2
For a typical chemical reaction with an energy change of 100kJ mol-1
1 x 105/(3 x 108)2 = mass change
Clearly this is so small as to be effectively zero. To all intents and purposes the law of conservation of matter is obeyed.