The study presents 1D discrete map (DM) to describe the dynamics of the oscillator with chaotic pulse position modulation (PPM). The model circuit has pulse voltage-controlled oscillator (PVCO) and feedback (FB) loop with a threshold of pulse rate coding, which performs nonretriggerable monostable multivibrator (MMV). DM is based on the analysis of this circuit using a simple approximation of the frequency modulation, which includes a threshold condition on the pulse period and sigmoid function of rate coding. The model circuit and DM demonstrate dynamic chaos in a wide range of control parameters. The transition to the chaos occurs by a jump either from a fixed point (tangent bifurcation), or from a limit cycle. An experimental (digital-analog) circuit of the chaotic pulse oscillator, in which the FB unit is MMV with a microcontroller (MC), is implemented. The relationship between the presented DM and the well-known sawtooth (Bernoulli) map (STM), widely used in engineering, is discussed.