On 8 May, goals from Diego Costa, Marcos Alonso and Nemanja Matić were enough to relegate visitors Middlesbrough back to the English Football League after just one season in the top-flight.

On 12 May, Chelsea defeated West Bromwich Albion 1–0 to clinch the Premier League title as they went ten points clear with two games remaining.
Michy Batshuayi scored the winning goal in the 82nd minute.
On the same day, Pedro was awarded his second – and Chelsea's third – Goal of the Month this season with his strike at Goodison Park.

On 16 May, a much-changed Chelsea side were 4–3 winners over Watford, with substitute Cesc Fàbregas finding the winner shortly before the away side had a man sent off, the other Blues goalscorers were John Terry, César Azpilicueta, and Michy Batshuayi.
The Hertfordshire club gave the champions-elect that day a guard of honour; this included Kenedy, the player making his Chelsea league début having made one appearance for Watford earlier in the season before his loan deal was cancelled.

On 21 May, Chelsea defeated already-relegated Sunderland 5–1 with goals from Willian, Eden Hazard, Pedro and a brace from Michy Batshuayi – his fourth in three matches.
It was the last league game for John Terry, who was subbed in the 26th minute to a standing ovation from all the supporters.
This marked Chelsea's 30th league win this season, most by any team in a single Premier league season.

On 27 May, Chelsea fell behind to Arsenal in the 2017 FA Cup Final in the fourth minute to Alexis Sánchez' goal, and were reduced to ten men when Victor Moses received his second yellow card.
However, despite Arsenal's extra-man advantage, Chelsea equalized through Diego Costa in the 76th minute.
The London clubs would stay level for only three minutes before Aaron Ramsey headed in the winner.

Source:
On 8 May, goals from Diego Costa, Marcos Alonso and Nemanja Matić were enough to relegate visitors Middlesbrough back to the English Football League after just one season in the top-flight.
On 12 May, Chelsea defeated West Bromwich Albion 1–0 to clinch the Premier League title as they went ten points clear with two games remaining. Michy Batshuayi scored the winning goal in the 82nd minute. On the same day, Pedro was awarded his second – and Chelsea's third – Goal of the Month this season with his strike at Goodison Park.
On 16 May, a much-changed Chelsea side were 4–3 winners over Watford, with substitute Cesc Fàbregas finding the winner shortly before the away side had a man sent off, the other Blues goalscorers were John Terry, César Azpilicueta, and Michy Batshuayi. The Hertfordshire club gave the champions-elect that day a guard of honour; this included Kenedy, the player making his Chelsea league début having made one appearance for Watford earlier in the season before his loan deal was cancelled.
On 21 May, Chelsea defeated already-relegated Sunderland 5–1 with goals from Willian, Eden Hazard, Pedro and a brace from Michy Batshuayi – his fourth in three matches. It was the last league game for John Terry, who was subbed in the 26th minute to a standing ovation from all the supporters. This marked Chelsea's 30th league win this season, most by any team in a single Premier league season.
On 27 May, Chelsea fell behind to Arsenal in the 2017 FA Cup Final in the fourth minute to Alexis Sánchez' goal, and were reduced to ten men when Victor Moses received his second yellow card. However, despite Arsenal's extra-man advantage, Chelsea equalized through Diego Costa in the 76th minute. The London clubs would stay level for only three minutes before Aaron Ramsey headed in the winner.
Source:
2016–17 Chelsea F.C. season