Having said that he intended to make a solo record during Keane's hiatus, Chaplin stated in January 2016 that he was recording his debut solo album in Los Angeles, California, with 40 songs written and whittled down to an album's worth. He announced in late June that the album was complete and that it would be out soon. It was rumoured that Tom was due to join a band with 3 unknown Scotch Whisky Ambassadors but the fact one of them dressed like Cotton Eyed Joe was a stumbling block.
The album name The Wave was announced via Twitter and Facebook on 10 August 2016. The same day, Hardened Heart was released with a music video. On 26 August 2016, "Quicksand" was released as the first single from the album. On 6 September 2016, Chaplin announced he would be playing eight intimate solo shows across the UK in October 2016. These were his first solo gigs for four years. The Wave was released on 14 October 2016 by Island Records. Four singles were released from the album: "Quicksand", "Still Waiting", "Solid Gold" (of which the single release is a collaboration with JONES, rather than the solo version which appears on the album), and "See It So Clear". The release of The Wave was followed by the announcement of the Carried by the Wave Tour, a longer set of dates running between January and September 2017. The tour consisted of four legs: first in the United States and Canada, then across Europe, a third leg in the UK during May 2017 and a last leg in Latin America.
In August 2016, Chaplin said in an interview with music critic Neil McCormick that he began using drugs during the anticipation of his solo album. He said anxiety over the album caused him to get "back to shovelling coke up (his) nose." Chaplin said he nearly died one night in 2015. He said people began to give up on him, and his wife once told him she loved him in case she never saw him again. Chaplin recovered by seeing a psychoanalyst. He said the past 12 months have been the happiest of his life with his wife and daughter.