The Blues were in control of the match but a number of missed chances meant they were always in danger of letting the game slip. Cesar Azpilicueta had given Chelsea the lead in he first half, attacking a loose ball in the six yard box with the help of some very bad defending on West Ham's part.
But after Alvaro Morata had two goals ruled out for offside, Javier Hernandez equalised for the Hammers.
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"We're definitely a really unsafe team", Hart told the club's website.
"(I think he has done) enough to get himself on the plane but not a starting place", Gale told Premier League Daily.
Hernandez said after the game that he hoped his goal had given manager David Moyes something to think about, but the Mirror suggests he is likely to move sooner rather than later.
"Like the last weeks again, we give them a gift". "It's such an important match for us and for all the good that came out of (last) Sunday, we only got one point and we want three points".
If West Ham can pocket £5million for a player who only has 15 minutes of first-team football for them, they should take it.
West Ham boss David Moyes was full of praise for the 75-cap England worldwide after his display at Stamford Bridge, insisting Hart has given Gareth Southgate a timely reminder of his global credentials.
Chelsea now sit fifth in the Premier League after a disastrous title defence.