That's a bit too simplistic. Are you postulating that a functioning nuclear chain reaction is discovered a short time after the chain reaction theory is discovered?
How about push the chain reaction theory back? Better than that, push the discovery of radioactivity back in history, as much as you can. That honor belongs to
Henri Becquerel. All you need is potassium uranyl sulfate, photographic plates and black paper. Fox Talbot invented the calotype process in 1840, I believe in doing so created plates that could capture the negatives you needed for the experience. By 1848, someone studying phosphorence in uranium salts could discover radioactivity, the idea that a material can emit a ray that passes through materials.
After that, see what you can come up with...
Errr... but that's not going to help much. For some considerable time after the discovery of radioactivity, no one knew what was going on. Einstein didn't come up with E=mc^2 until special relativity in 1905, which was a development unrelated to radioactivity at all.
Let's back up a bit. Maxwell's equations were published together until 1884. Light as electromagnetic radiation wasn't predicted until 1865, and not experimentally demonstrated until 1887. Lorentz contractions are a consequence of Maxwell's equations, but not taken seriously.
Personally, I doubt that E=mc^2 could have realistically happened perceptibly earlier than it did. I think only the specific genius of Einstein allowed it to happen that early.
So, suppose you have 'radioactivity', Maxwell's equations, maybe even E=mc^2.
Your next problem is that the theory of what an atom was and looked like wasn't developed either. The electron wasn't discovered until 1897; JJ Thompson, its discoverer, thought the atom looked like a plum pudding with electrons studded through the body like fruit in a pudding. Rutherford's 'solar system' model was followed Bohr's model and then the Electron Cloud
http://www.csmate.colostate.edu/cltw/cohortpages/viney/atomhistory.html
And we still have no clue as to what's going on in the center. Chadwick didn't discover the neutron until 1932.
You CAN'T have a theory of neutron chain reactions if you haven't discovered neutrons.
Really, there is a WHOLE lot of physics (let alone chemistry and engineering) that needs to be developed before an A-bomb is possible. You are NOT going to get it much earlier than OTL. One year, sure. Two, with some work. Three? needs a number of things to go just right. I think 4 or 5 years earlier requires either massive changes in the development or possibly ASBs.
Sorry.
Nuclear weapons are hard. They require large amounts of modern physics. Significant amounts of modernish math. Lots and lots modern chemistry and probalby industry. Lots of modern money.....