Due to the high energy efficiency per bit and high sensitivity, Return-to-zero differential-phase-shift-keying (RZ-DPSK) is perfectly suitable for free-space laser communications. However, the conventional generation method of RZ-DPSK optical signal requires two modulators, which is costly, bulky, and heavy, significantly hindering the application of RZ-DPSK in size, weight, and power (SWaP)-constrained satellite platforms. In this paper, we propose and experimentally demonstrate a modulator-free variable multi-rate RZ-DPSK free-space optical (FSO) communication system based on chirp-managed laser (CML). Based on the proposed scheme, an FSO outfield experiment over 1 km has been successfully undertaken, achieving receiving sensitivities of -48.9 dBm and -45.6 dBm at 2.5 Gbps and 5 Gbps, with bit error rate (BER) of 1 x 10(-3) without forward error correction (FEC), respectively. The performance of the proposed system is also investigated by studying the eye diagrams under two different test conditions of back-to-back transmission and 1-km free space transmission. In addition to the small size, lightweight and low cost, the proposed scheme shows great potential for a variety of FSO communication applications ranging from Cube-Star to larger satellite laser communication platforms.