Transport Layer Security (TLS) provides a secure channel for end-to-end communications in computer networks. The ChaCha20–Poly1305 cipher suite is introduced in TLS 1.3, mitigating the sidechannel attacks in the cipher suites based on the Advanced Encryption Standard (AES). However, the few implementations cannot provide sufficient speed compared to other encryption standards with Authenticated Encryption with Associated Data (AEAD). This paper shows ChaCha20 and Poly1305 primitives. In addition, a compatible ChaCha20–Poly1305 AEAD with TLS 1.3 is implemented with a fault detector to reduce the problems in fragmented blocks. The AEAD implementation reaches 1.4-cycles-per-byte in a standalone core. Additionally, the system implementation presents 11.56-cycles-per-byte in an RISC-V environment using a TileLink bus. The implementation in Xilinx Virtex-7 XC7VX485T Field-Programmable Gate-Array (FPGA) denotes 10,808 Look-Up Tables (LUT) and 3731 Flip-Flops (FFs), represented in 23% and 48% of ChaCha20 and Poly1305, respectively. Finally, the hardware implementation of ChaCha20–Poly1305 AEAD demonstrates the viability of using a different option from the conventional cipher suite based on AES for TLS 1.3.