Chamber finance was the system of English finance which replaced the Exchequer
during the reign of Edward IV
The Exchequer was the traditional centralisation point for the King's money in medieval times. All the money from the Duchy of Lancaster, as well as that from taxes, customs and duties. The money was counted and processed by officials, but there was a huge opportunity for embezzlement - sufficient records were not kept, and the King could not directly supervise the process.
Edward IV essentially moved the Exchequer into his bedroom. The royal funds were kept in a room behind his personal chamber, and he kept a close eye on incoming money and outgoings. There wasn't any more sophisticated book-keeping, but as everything was happening under the King's nose embezzlement was unlikely. To further reduce the risk, the King put one of his most trusted advisors - the Lord Chamberlain - in charge of the money.
Richard III continued to use the policy of chamber finance when he seized the throne. When Henry VII, a King noted for his financial mind, came to power however, he did not appear to recognise the effectiveness of this system, and moved the control of finance back to the Exchequer. In the first year of his reign he only managed to collect half the money Richard III had in his last year, so he quickly reverted back to chamber finance.