Probably depends on how broad your definition of toothbrush. If we look at a toothbrush in its essential form we can come to the conclusion that it is an instrument to clean ones teeth. If we start with this definition than we can see the first toothbrushes coming from Babylonia from around 3500 B.C. they used some kind of chewing stick to clean their teeth. The first 'real' toothbrush we can find in china in the 17th century. The Romans and Greek also know the importance of dental hygiene. They used toothpicks and twigs.^1 To go even further rich romans may have had slaves to take care of their teeth^2 The chinese toothbrush however was reinvented by europeans in the 18th and 19th centuries. The first patent on the other hand was claimed by a certain Mr Wadsworth in the US.^1 When toothbrushes were unleashed on America in the early 20th century it was common for poor families to share one toothbrush. In the 1930s however toothbrushes were much cheaper due to change in materials i.e. plastic instead of wood. This made sure that most people could afford one toothbrush per person. Those first toothbrushes were made from ivory handels and the manes of horses^3 I highly advice to read some of the links I provided below if you can read them. They're highly intersting if you like the history of the toothbrush.

Sources: ^1 http://www.scielo.br/scielo.php?pid=S1806-83242009000500004&script=sci_arttext ^2 http://europepmc.org/abstract/MED/12846261 ^3 http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0757.1997.tb00099.x/abstract