The visiting Generals have games in hand on most around them thanks to their Emirates FA Cup run and were looking to put pressure on the play-off places themselves. However, Frome came into the game on a run of six league and cup games without defeat, but with a long injury list.
They broke the deadlock by taking a 36th minute lead via a free-kick from Connor Roberts from near the halfway line which somehow found its way into the back of the net. And the home side went into half-time two-up, thanks to a 43rd minute Jon Davies effort.
Chesham battled hard to get back into the game in the second period but the Somerset outfit held firm.
Follow the EVO-STIK League Southern on Twitter at @SouthernLeague1
Keep up-to-date with our exclusive email newsletters.
Subscribe