Dynamic subtraction game
Hint: A player loses if they are presented with a pile of size 1. If presented with a larger pile, what should you do if it's the first move of the game?



Here is a more general solution, which will be applicable in other cases.

You can find the winner (and even the Sprague-Grundy function) using dynamic programming. Each state of your game consists of a pair $(n,B)$, where $n$ is the number of chips, and $B$ is an upper bound on how many chips you're allowed to remove. I'll let you figure out the edges of this dag and the starting state. Now you scan the graph from the sinks up: a sink (state with no outgoing edges) is a LOSE state (from the point of view of the player whose turn it is to play). A state leading only to WIN states is a LOSE state, otherwise it's a WIN state, and any edge pointing at a LOSE state is a winning move.

It's probably more challenging to find a general formula for which player wins the game given $n$, but one way would be to compute it empirically for several values of $n$ (or more generally, of $n$ and $B$), figure out a formula, and prove your formula.