Tauranac chose a conservative approach for the BT3 at a time when Lotus had already introduced monocoque construction with the Lotus 25. Rather than follow that trend, the BT3 used an exceptionally stiff steel-tubed spaceframe chassis, which Tauranac reasoned would be easier to repair and closer to what Motor Racing Developments was selling to customers. The cockpit was comparatively spacious for the era, with oil and water cooling pipes routed outside to keep heat manageable. A fibreglass body shell in bright turquoise with a metallic gold stripe clothed the chassis.
Power came from Coventry Climax's 1,494 cc FWMV V8 engine, producing around 157 bhp in 1962 trim and approximately 190 bhp in its 1963 form. Drive was transmitted through an Alf Francis-designed Colotti six-speed gearbox — technically sophisticated but prone to fragility in competition. Suspension was fully independent double wishbone at all four corners, with 13-inch wheels initially. The original 9-inch disc brakes proved insufficient and were enlarged to 10.5-inch units at the front after only the second race, which also necessitated a switch to 15-inch front wheels.
Only one Formula One-specification BT3 chassis was built, numbered F1-1-62. Its design served as the template for the Brabham BT4, fitted with 2.5 and 2.7-litre Climax FPF four-cylinder engines for the Intercontinental Formula and Tasman Series.
The BT3 arrived too late for the earlier rounds of the 1962 World Championship, with the team using a Lotus 24 in its place. The new car was to have debuted at the British Grand Prix, but a wrong exhaust system discovered at 3 am before the race prevented it. After brief shakedown tests at Goodwood and Brands Hatch, the BT3 was shipped to the Nürburgring for the German Grand Prix. The debut was troubled — an engine failure in practice forced Jack Brabham to qualify 24th using a spare unit assembled from scavenged components. An overnight engine change got a fresh unit into the car, but improvised throttle linkage caused problems and Brabham retired after nine of fifteen laps.
Better results followed. At the Oulton Park International Gold Cup, Brabham qualified fifth and finished third despite nursing worn brake pads, taking his first podium in a car bearing his name. At the final two Championship rounds — the United States and South African Grands Prix — he finished fourth at both, scoring the Brabham marque's first Constructors' Championship points. Between those events, Brabham finished second in the inaugural Mexican Grand Prix, the only driver on the same lap as joint winners Jim Clark and Trevor Taylor.
The BT3 was officially replaced for the 1963 Championship season by the new Brabham BT7, though Brabham himself pressed it into service for the Belgian and Italian Grands Prix when a BT7 chassis was unavailable. The car's most significant victories came in non-Championship events: Brabham won both the 1963 Solitude Grand Prix and the 1963 Austrian Grand Prix in the BT3, marking the first race wins for his team's own cars and the first time a driver and constructor sharing a name had won a Formula One event. At Zeltweg, Brabham and the BT3 finished five full laps ahead of second-placed Tony Settember while Lotus and Cooper challengers retired on the rough airfield circuit surface. Brabham also loaned the car to his young mechanic Denny Hulme, a future Formula One World Champion, who drove it to fourth in the 1963 Kanonloppet in Sweden.
Prior to the 1963 season the BT3 had been lightened by 55 lb, the chassis lowered, and its livery changed from turquoise-and-gold to the dark green and gold that would become Brabham's signature colours for the rest of the decade. The car was also used as a development mule for the BT7.
At the end of 1963, the BT3 was sold to Brighton-based privateer Ian Raby, who replaced the Climax engine with a BRM V8 unit and continued to enter the car in occasional Formula One races through 1964 and 1965 without scoring Championship points. When Raby sold the car to David Hepworth in 1965, the BRM engine was removed in favour of a 4.7-litre Chevrolet V8, and the BT3 competed in Formule Libre and hillclimb events in 1966.
The unique chassis survives to the present day. It was subsequently restored to its original 1962 Formula One specification, complete with the turquoise-and-gold livery, and for many years was part of the Donington Grand Prix Exhibition museum collection.
The BT3 established several firsts that gave the Brabham name its early identity: the first Championship points, the first race win, and the first podium under that marque. Its conservative but robust engineering philosophy, championed by Ron Tauranac, reflected a pragmatic approach to racing car design that would characterise Brabham's customer-focused operations throughout the 1960s. The car's lineage flowed directly into the BT4, BT7, and the succession of designs that brought Brabham consecutive Constructors' Championships in 1966 and 1967.