We present a memory array of organic ferroelectric field-effect transistors (OFeFETs) on flexible substrates. The OFeFETs are connected serially, similar to the NAND architecture of flash memory, which offers the highest memory density of transistor memories. We demonstrate a reliable addressing scheme in this architecture, without the need for select or access transistors. As proof of principle, a 1 x 4 NAND-like string is fabricated and characterized. Retention up to one month and endurance up to 2500 cycles are shown. Read and write disturb measurements show that the memory array can potentially be scaled up to 8 kbits.