Well. maybe not a practically usable transmitter, but it does produce a few mW of RF power at 4 MHz using only two LMC555s.
Note that no other semiconductors were harmed in the creation of this project.
Theory of Operation (Refer to attached simplified schematic):
At lower operating voltages the LMC555 's Trigger (TR) input can be used like an inverting comparator input to control the device's output. This requires that the Threshold (TH) input be active (high).
This circuit applies a DC bias at TR's switching threshold and superimposes a small AC feedback signal to produce an oscillator.
An inverted version of the same signal is applied to a second LMC555 to produce two complementary open-collector outputs (the Discharge outputs of the devices).
The outputs are then connected as a standard push-pull RF amplifier.
The TH input serves as an Enable input to key the transmitter.