The German chemist August Kekulé gets the credit, but both he and and the Scottish chemist Archibald Scott Couper developed the theory of chemical structure in 1858.
In 1857 Kekulé announced that carbon is tetravalent.
On May 19, 1858 he announced that carbon atoms link to each other, and he extended this idea to the bonding order of all of the atoms in a molecule.
At the same time, the Scottish chemist Archibald Scott Couper was studying under the Alsatian French chemist Adolphe Wurtz (developer of the Wurtz synthesis).
He independently developed the concept that tetravalent carbon atoms link together and that the bonding order of the atoms in a molecule can be determined from chemical evidence.
He presented his paper to his supervisor in early 1858, but Wurtz was so slow in submitting it that it did not appear in print until June 14, 1858.
So Kekulé gets the credit for being the first person to develop structural theory, because he published about four weeks before Couper.
But Couper devised the first molecular formulas in that showed bonds connecting the atoms.
For example, his structure of propan-1-ol was
Note: The formula contained two O atoms because chemists of the day thought that the atomic mass of O was 8.