West Ham have exceeded expectations so far this season and sit fourth in the Premier League table after losing only four of their first 17 matches.
Allardyce's men beat bottom-of-the-table Leicester City on Saturday and have now won four of their last five top-flight games.
Leaders Chelsea are their next opponents on Boxing Day, with Arsenal visiting Upton Park two days later.
West Ham held Jose Mourinho's side to a goalless draw when the two sides met at Stamford Bridge last season and Allardyce is not fearing a trip to west London.
He told the club's official website: "It's a nice time to be playing Chelsea and Arsenal. Our draw away at Chelsea last season was our turning point, from then we kicked on and stayed up. So it was huge.
"They're two tough games but we have earned the right to have a go at both them.
"The cream on top of our cake this season has been the wins over Manchester City and Liverpool so we know we're capable of getting something from these games."
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