**Yes, Greenland and China have a relationship, primarily economic and strategic, though it is limited and often indirect (mediated through Denmark, as Greenland is an autonomous territory within the Kingdom of Denmark).**
### Key Aspects
- **Economic Interests and Investments** → China has pursued opportunities in Greenland's rich rare earth minerals, mining, fishing, and tourism sectors. Chinese companies (e.g., Shenghe Resources) hold stakes in projects like the Kvanefjeld (Kuannersuit) rare earth mine. Greenland views China as a potential partner for development and greater independence.
- **Infrastructure and Arctic Strategy** → In the 2010s–2020s, China expressed interest in funding airports, naval stations, and other projects as part of its Arctic ambitions, but many were blocked due to security concerns from Denmark and the US.
- **Diplomatic Ties** → No direct formal embassy-level relations exist between Greenland and China. Diplomatic affairs are handled by Denmark, which has full relations with China since 1950.
- **Geopolitical Context** → China's involvement has strained Denmark-Greenland relations and drawn US attention (e.g., recent comments amid US interest in Greenland's security). China positions its activities as cooperative, while others view them through an Arctic power lens.
The relationship is asymmetric: China seeks resources and influence in the Arctic, while Greenland seeks investment for growth. It's not a deep alliance but notable in geopolitical discussions.