Braney, who joined the Hatters in the summer from Isthmian Premier club Bowers & Pitsea, has been a regular on the scoresheet for the Town development squad this season.
The 18-year-old will look to gain more senior experience at The Meadow with a side who are currently third in the table and seeking to gain promotion to National League South. He could make his debut when Chesham face Salisbury on Saturday.
Good luck in your time as a General, Tobias!