This question seems pretty tricky for one to provide straightfoward answer to. First of all, egg is layed by chicken which requires it to be hatched by the chicken. In other words, without chicken, egg cannot be layed and hatched. So therefore, there must be the presence of chicken for the egg layed to be brooded, hatched and become a chick that'd definitely grow up to become chicken.
Now let's look at the situation whereby there is no chicken. Meaning that there can never be egg. And let's take for example, there is egg and there's no chicken to hatch it, how can such egg be hatched? Except maybe through the use of artificial means which is the use of incubator. And before the use of this artificial method of hatching eggs into chicks, there must be the availability of chicken to lay these eggs.
From the above analysis, we all can deduce that chicken came first before the egg because without chicken there can never be egg.