This paper is devoted to software-defined radio (SDR) implementation of frequency modulated antipodal chaos shift keying (FM-ACSK) transceiver and presents results of prototype testing in real conditions. This novel and perspective class of spread-spectrum communication systems employs chaotic synchronization for the acquisition and tracking of the analog chaotic spreading code and does not need resource-demanding cross-correlation. The main motivation of the given work is to assess the performance of FM-ACSK in real conditions and demonstrate that chaotic synchronization can be considered an efficient spread-spectrum demodulation method. The work focuses on the real-time implementation aspects of the modulation-demodulation algorithms, forward error correction (FEC) and symbol timing synchronization approach in MATLAB Simulink. The performance of the presented prototype is assessed via extensive testing, which includes measurement of bit error ratio (BER) in single-user and multi-user scenarios, estimation of carrier frequency offset (CFO) impact and image transmission over-the-air between two independent sites and comparison with classical frequency hopping spread spectrum (FHSS). The paper shows that the presented class of the spread spectrum communication systems demonstrates good performance in low signal-to-noise ratio (SNR) conditions and in terms of BER significantly outperforms the classic spread-spectrum modulation schemes which employ correlation-based detection.