Ditch the chain. You think straps are bad, you should see what happens when chains cut loose. Pick up one of the HD tow straps from Tractor Supply or somewhere...you should be able to find straps rated up to something like 20K#.
Also, a snatch strap would be better anyway for pulling someone out of mud or snow, vs a non-elastic tow strap...the non-elastic ones are better for spotting, truck wrangling and slow steady pulls like if you need to gently ease someone off a rock pile.
ARB, Black Rat, probably Warn, and others make good snatch straps, and there was a comparison article floating around a year or so ago. They aren't always cheap, but then neither is a Tundra! Don't skimp on this
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-Sean