Making his screen acting debut in the 1988 television film Quiet Victory: The Charlie Wedemeyer Story, Chandler's first regular television role was in the ABC drama Homefront (1991–1993). This was followed by the lead role of Gary Hobson in the series Early Edition (1996–2000). His well-received guest appearance on the medical drama Grey's Anatomy (2006–2007) earned Chandler his first Primetime Emmy Award nomination.
Chandler's film work has included notable supporting roles in King Kong (2005), The Day the Earth Stood Still (2008), Super 8 (2011), Argo, Zero Dark Thirty (both 2012), The Wolf of Wall Street (2013), Carol (2015), Manchester by the Sea (2016), Game Night and First Man (both 2018), Godzilla: King of the Monsters (2019), Godzilla vs. Kong (2021). Chandler has also starred in the Netflix thriller series Bloodline (2015–2017), for which he received further Primetime Emmy Award nominations.