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Neutrons were discovered by James Chadwick in the year 1932.
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If you understand Particle Physics, then I must tell you that a neutron is made up of two down quarks and one up quark.
A down quark has a charge of -1/3, So two down quarks have a charge of -2/3
And an up quark has a charge of +2/3
Adding them up, we get 0
So, neutrons are neutral
James Chadwick discovered the Neutron in 1932.

However, the existence of a neutral particle inside the nucleus had been predicted by Rutherford earlier.