Yes, chemical reactions can happen anywhere- even in space. But, reactions are highly dependent on temperature. In space, the range of temperature varies. For example, near the Sun the temperature is several thousands of Fahrenheit whereas towards the outer end it is minus several hundreds Fahrenheit. So the reactions rate (speed at which reaction comes to completion) will vary depending on the temperature conditions.
Space also consists of other forms of energy like cosmic rays, ultraviolet rays etc which can give enough energy for chemicals to react.
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