However, the Hammers did eventually get one back, with Manuel Lanzini slotting home from an Andre Ayew pass.
"I'm really happy with the way we started", he said.
West Ham are optimistic that striker Andy Carroll, who has been out for a month with a groin injury, will be fit to make his comeback on Monday.
Moses cleared a shot off the line as the visitors came out unscathed from a rare West Ham attacking surge, before Randolph made a superb save in the 66th minute from Costa after a great turn by the Spaniard. From there, he kept composed to give Chelsea the lead. Antonio Conte's plan of sitting deep and breaking with blistering pace was working a treat.
Remember when Chelsea went winless in September, and some questioned whether Antonio Conte was the right manager?
Since a switch to a 3-4-3 formation by Conte, the Blues have almost been unstoppable. Only one team in the last 10 years has had more points than Chelsea at this point, and that was 2012-13 Manchester United.
And after nearest challengers Tottenham and Manchester City both won at the weekend, Blues boss Conte was delighted to see his players hold their nerve.
Chelsea again showcased their versatility, tenacity and bags of quality in the final third.
West Ham United's Victor Moses (right) and West Bromwich Albion's Gareth McAuley battle for the ball during the Barclays Premier League match at The Hawthorns, West Bromwich.More news: Where you can buy a Nintendo Switch on launch day?
"I'm pleased for my players, it's not easy to play after your opponents played and won", he said.
'I think sometimes when I'm on the pitch I see him twice.
"We will try to win trophies as soon as possible".
This, too, was further evidence that this team has completely bought into what Conte is looking to achieve at Stamford Bridge, none more so than Cesc Fabregas who has worked his way back into the fold, reinventing his game to satisfy his demanding coach enough to be rewarded with a starting role.
Conte hailed the way his players managed the game, at least until the latter stages.
"They showed me great will to win the game and to suffer in the first part of the first half, but stay compact because we didn't concede great chances for West Ham to score". It's a pity to give away a second clean sheet at the end of the game, the second after Arsenal - we must work a bit on this aspect.
Still, they are now two points worse off than that team from 12 years ago, and are nowhere near as watertight defensively, conceding a whole 12 goals more.
Recently, a draw away to Burnley certainly wasn't the end of the world: Sean Dyche's side have a stunning home record, and Chelsea didn't need to go for broke to win anyway. We must improve in this situation.