Which currency is pegged to the US dollar in a narrow band around 7.8?

The currency pegged to the US dollar in a narrow band around 7.8 is the Hong Kong dollar.

Hong Kong operates a linked exchange rate system in which the Hong Kong dollar is maintained between HK$7.75 and HK$7.85 to US$1. The central reference rate is commonly described as HK$7.80 per US dollar, which explains the wording of the question.

The system was introduced in 1983 after severe pressure on Hong Kong’s currency during a period of financial and political uncertainty. It is based on currency-board principles: changes in the monetary base are backed by corresponding changes in US-dollar reserves. The Hong Kong Monetary Authority supports the arrangement through convertibility undertakings rather than managing the currency like a freely floating exchange rate.

The band is not the same as a permanently fixed single price. Since 2005, the HKMA has provided a strong-side level of 7.75 and a weak-side level of 7.85. The Taiwanese dollar, Chinese yuan and Singapore dollar may respond to the US dollar, but none matches this distinctive Hong Kong arrangement.