Jose Mourinho's men progressed to the semifinals of the Champions League midweek, with Demba Ba scoring late to secure a 2-0 second-leg victory over Paris Saint-Germain that put the Blues through via the away goals rule.
However, a trip to the Liberty Stadium in the Premier League may not fill the Londoners with confidence as they turn their attentions back to the domestic title race.
Chelsea has been held to draws in each of its previous two league fixtures at Swansea and, last season, its hopes of Capital One Cup glory were ended in a dramatic semifinal second-leg encounter in south Wales.
It would be fair to assume that Charlie Morgan — the ball boy involved in that incident — will not be on duty Sunday, while Hazard is also likely to be absent after picking up a calf problem against reported suitor PSG in midweek.
Chelsea currently sits two points adrift of Premier League leader Liverpool, while third-place Manchester City, which visits Anfield in the undoubted match of the weekend earlier Sunday, is a further two points back with two games in hand.
Mourinho's charges cruised to a 3-0 win over Stoke City in its last league outing, while Swansea — just six points clear of the relegation zone — slumped to a lackluster 1-0 defeat at FA Cup semifinalist Hull City.
Chelsea's last Premier League away trip produced a disappointing 1-0 defeat at Crystal Palace — its third loss in a row on the road in all competitions — but Swansea coach Garry Monk is keen not to underestimate the challenge that his side faces.
"Chelsea are competing for the league, [are] in the semifinals of Champions League and have one of the strongest squads and best managers in the world," Monk told the press. "When you look at it like that, we don't have a chance — but you don't think like that, it's something we embrace and it's a chance to showcase what we can do. We have to be confident."
Swansea has no fresh injury concerns but Dwight Tiendalli's illness means that Angel Rangel's starting berth looks unlikely to be in doubt, despite the player being openly criticized by Monk for his performance last week.
Aside from question marks over the fitness of Hazard, Mourinho should have a full squad at his disposal, although John Terry is a doubt with a foot injury.
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