How can you have multiple colours in a single lore line?

I am trying to make a long description of an item, with multiple colours:

give @p leather_chestplate{display:{Lore:'[{"text":"It is","color":"gray"},{"text":" SUPREME","color":"light_purple"}]'}}

With all of my past trials, either SUPREME is on the next line, or it doesn't work. Why isn't it working and what can I do to fix it?

You are so close! You are almost correct in that you're trying to put the Lore tag as a single string so that it will appear in one line, but you forgot that the Lore tag is a list by default, in case additional lines need to be added. Even if you are only planning to have one line, the Lore tag still has to be a List tag.

Incorrect way:

{
  display: {
    Lore: '[{"text":"It is","color":"gray"},{"text":" SUPREME","color":"light_purple"}]'
  }
}

Correct way:

{
  display: {
    Lore: [
      '[{"text":"It is","color":"gray"},{"text":" SUPREME","color":"light_purple"}]'
    ]
  }
}