Low probability of detection (or covert) communication refers to the scenario where information must be sent reliably to a receiver, but with low probability of detection by an adversary. Recent works on the fundamental limits of this communication problem have established achievability and converse bounds that are asymptotic in the block length of the code. This paper uses Gallager's random coding bound to derive a new achievability bound that is applicable to low probability of detection communication in the finite block length regime. Further insights are unveiled that are otherwise hidden in previous asymptotic analyses.