Any non-practical 4x4 vehicle. The etymology is of course the sarcastic suggestion that this "tractor" is for a farmer in the London borough of Kensington and Chelsea, and is unlikely to get mud on it unless deliberately applied with a brush.*
The classic Chelsea Tractor is the Range Rover. It's enormous, hideously expensive, drinks tremendous amounts of fuel and is very rarely used by anyone involved in agriculture or rural pursuits because of these attributes. For this reason, it has become the prototype for an entire class of 4x4 vehicles driven exclusively by stupid rich people who live in cities.
Spiritual descendants which also fit the Chelsea Tractor mode include the Toyota RAV4, the BMW X5 (a car which is actually utterly useless off-road and gets mud into its air intake), the Land Rover Discovery and its little sister the the Freelander, the Mitsubishi Shogun, the Isuzu Trooper, that great big Lexus RX, the VW Touareg, the GM Frontera and Montera and anything Ford decide is off-road-capable, especially the Ranger which is actually usually only sold as a 2wd anyway.
Chelsea Tractors are very popular on the school run because they cause the maximum amount of blockage to other traffic, show off stupid amounts of money and are utterly impractical and do worse on all safety ratings than your average hot hatch. As well as vulgar ostentation, Chelsea Tractors are useful for taking Pippa to ballet class because one never knows whether there'll be a slick of Ribena on the way over Hampstead.
*Thanks to StrawberryFrog for the reminder.
*Wertperch has sighted cans of spray-on mud for the Chelsea Tractor driver with the grace to be embarassed about it.